content.njctl.orgcontent.njctl.org/.../probability-cw-and-hw-2016-01-05.d… · Web view32. If...

SetsClass Work1. Draw a sample space for the following situations:

a. Rolling a set of two dice and multiplying the numbers on each to find an answer.

b. Drawing two marbles out of a bag, with replacement. Out of 20 marbles, 4 are red, 10 are blue and the rest are yellow.

c. Spinning a spinner with the numbers 1 through 8 on it.

2. On the back of this worksheet or on another piece of paper, draw a Venn Diagram that compares the choices of candy between a group of boys and a group of girls on a field trip. Use the following information. The boys and their choices are as follows: Logan chose licorice and toffee, Arik chose gum and Snickers, Jim chose licorice and Snickers, Rob chose toffee and Reese’s and Bill chose gum and mints. The girls and their choices are as follows: Tess chose mints and Skittles, Brianna chose Skittles and Mounds, Paige chose Starburst and Snickers, Katie chose toffee and Snickers and Grace chose Skittles and Starburst.

3. Use the Venn Diagram below to answer the questions.

a. Name the Universe for the problem.

b. Name all three of the sets involved.

c. Find: i. A∩B ii. BUC iii. A∩(BUC) iv. ~(BUC)∩A

v. ~(AUB) vi. A∩B∩C vii. AU(B∩C) viii. (AUB)∩~C

4. The following Venn Diagram shows the results of a college survey about extra-curricular activities that men (A) and women (B) do regularly. Use this diagram to list the members of the following sets and then write a sentence to describe the result.a. U b. A∩Bc. A∩(~B)d. AUBe. ~Af. ~(A∩B)

Algebra II – Statistics and Probability ~1~ NJCTL.org

SetsHome Work5. Draw a sample space for the following situations:

a. Drawing a card from a normal deck of cards. Take only the different suits into consideration.

b. Rolling a single, six-sided die AND then flipping a coin.

c. Flipping a coin AND then spinning a spinner with the numbers 1 through 4 on it.

6. On the back of this worksheet or on another piece of paper, draw a Venn Diagram that represents the following situation. At USA High School, from a survey of 100 people, a student found that 90 had a TV, 40 had a laptop computer and 30 of those same people had both a TV and a laptop.




c. Find: i. A∩B ii. BUC iii. A∩(AUC) iv. ~(A∩C)∩B

v. ~(AUC) vi. A∩(BUC) vii. A∩B∩C viii. BU(A∩C)

8. The following Venn Diagram shows activities that male (A) and female (B) teens in Colorado do on the weekends. Use this diagram to list the members of the following sets and then write a sentence to describe the result.a. U b. A∩Bc. A∩(~B)d. AUBe. ~Af. ~(A∩B)

Spiral ReviewSimplify: Simplify: Factor: Simplify:


9. √36m8n6 10. −12x−6 y6

18 x−6 y−7 11. 24x3 – 36x 12.

1x4

1x6

Independence and Conditional ProbabilityClass Work13. Label the events as dependent or independent:

a. Your family decides to take a trip to Disney World for spring break. Your friend’s family decides to go to Disneyland.

b. You secretly take out all of the Aces from a deck of cards and then get your friend to see how many tries it takes to get an Ace.

14. Decide if the following events are mutually exclusive or overlapping. Then find P(AUB).

a. A = Drawing a red card from a regular deck of cards B = Drawing a face card from a regular deck of cards

b. A = Rolling an odd number on a six-sided die. B = Drawing a spade from a regular deck of cards

15. Find the conditional probability for the following problems:

a. Find the probability that it is raining, given that it is cold.

b. A bag contains different colored disks that are numbered from 1 to 10. The probability that the disk is green is 0.6. The probability that it is green and odd is 0.3. What is the probability that the disk is odd, given that it is green?

16. Use the formula P (B|A )P (A )

=P(B) to mathematically decide if the events are independent.

a. Rolling a 10 on a set of six-sided die and then rolling a 5.

b. A = taking math during your senior year at high school B = going to college


Independence and Conditional ProbabilityHome Work17. Label the events as dependent or independent:

a. The cost of a person’s insurance is high. Looking at the person’s driving record, they have had a lot of accidents.

b. You drink two 40oz. sodas a day for three weeks. In that time, you gain 15 pounds.


a. A bag of 15 marbles has 3 red marbles, 3 blue marbles, 3 yellow marbles, 3 green marbles and 3 black marbles. A = Drawing a red marble B = Drawing a blue marble

b. Using a regular deck of cards: A = Drawing an even numbered card B = Drawing a heart


a. Find the probability that a student is in a band, given that they take a music class.

b. Find the probability that a student gets good grades, given that they play a sport.



a. The probability that a person owns the car they drive, i.e. no payments, in USA High School is 40%. The probability that the person owns their car and knows how to change the oil is 35%. Decide if the events are independent and then find the probability that a person at USA High knows how to change the oil on a car, given that they own the car.

b.


Spiral ReviewFactor: Factor: Simplify: Simplify:

21. 125x3 – 27y322. 16m2 – 81 23. √24 r4 p8 24.

6n3m

Permutations & CombinationsClass Work25. For lunch, the school cafeteria has a selection of 4 entrees, 5 sides, 5 drinks, and 4 desserts. Assuming that you select one item from each category, how many different lunches could be made?

26. An electronics store is selling new televisions. The different choices include: rear projections, LCD, DLP, CRT, or plasma; full screen or wide screen; 13”, 19”, 27”, 32”, 36”, 41”, 51”, or 63”. How many different televisions does the store have to offer?

27. How many 4 digit numbers can be made using the digits 3, 6, 7, and 8 if the numbers cannot be repeated?

28. In how many ways can you select a committee of 5 students from a pool of 10 students?

29. In a certain country, the license plate is formed by 4 digits from 1 to 9 followed by 3 letters from the alphabet. How many license plates can be formed if neither the digits nor the letters are repeated?

30. The manager for a retail store must decide which sweaters to stock for the upcoming fall season. A sweater from one manufacturer comes in 5 different colors and in 3 different textures. The manager decides that the store will that the store will stock the sweater in 3 different colors and 2 different textures. How many different types of sweaters can the store choose to stock up on for the upcoming fall season?

31. A committee of 4 students is to be chosen from a group of 8 students. Barbara, Jack, Anna, and Connor are students in the group. What is the probability that all 4 of them will be chosen for the committee?

32. If the letters in the word LIBERTY are arranged at random, and no repetition is allowed, what is the probability that the first letter is a “T”?


33. When playing a game of poker, each player is dealt 5 cards from a standard deck of 52. A flush is when all 5 of the cards are of one suit. There are 4 suits in each deck. What is the probability of getting dealt a flush?

34. A 4 digit number is formed from the numbers 1, 2, 3, 4, 5, 6, and 7, with no repetitions. What is the probability that the number will be between 2,000 and 6,000?

Permutations & CombinationsHomework35. Wal-mart has a selection of batteries that you could purchase. The brands that are offered include EverReady, Duracell, Energizer, or Ray-O-Vac. After selecting the brand, you have to decide whether to get alkaline or non-alkaline batteries. Finally, you must select the size: AAA, AA, C, or D. How many different kinds of batteries are available for you to buy?

36. You wake up in the morning and go to the pantry to look for breakfast. You have a choice of Pop-Tarts, muffins, granola bars, or cereal. To drink, you have a choice of whole milk, 2% milk, skim mil, orange juice, apple juice, and water. Your mother insists that you take a multi-vitamin with your breakfast. You can choose from Flintstones vitamins, One-a-Day vitamins, or Chock’s Vitamins. How many different breakfasts made up of an entree, drink and vitamin could you make?

37. At the beginning of the summer, you have 6 books to read. In how many ways can you read the 6 books?

38. Five students from the 90 students in your class not running for class president will be selected to count the ballots to determine who wins the presidential race. In how many ways can the 5 students be selected?

39. A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committees can be formed from this group?


41. If the letters in the word HEPTAGON are arranged at random, and no repetition is allowed, what is the probability that the first letter is a “P”?

42. A committee of 4 students is to be chosen from a group of 6 students. Mike, Billy, Kendra, and Sarah are students in the group. What is the probability that all 4 of them will be chosen for the committee?

43. A 4 digit number is formed from the numbers 1, 2, 3, 4, 5, and 6 with no repetitions. What is the probability that the number will be between 1,000 and 3,000?


44. When playing a game of poker, each player is dealt 5 cards from a standard deck of 52. A pair is when 2 cards are the same. What is the probability of getting dealt a pair of any card?


Measures of Central TendencyClass WorkFor questions 45-47, find the mean, median, mode, range, IQR and the standard deviation of each set of data. Then, make a quantitative statement about each data set based on the measures of central tendency. Be sure to include something about the spread of the numbers.45. Test scores for a physics exam: (in percentages)

96 43 88 97 75 75 76 75 78 75

46. Top ten time results for a Men’s Giant Slalom race: (in seconds)85.18 85.38 86.48 87.04 87.31 87.40 87.43 88.22 88.38 88.56

47. Women’s Spring Board Diving Results: (total points) 414 379.20 362.40 362.20 345.65 343.00342.85 332.10 317.80 316.80 309.40 295.20

48. The table below shows a frequency of test scores on a math test. Find the mean.

49. Which number would you remove from the list below to get a smaller standard deviation?78, 78, 90, 99, 77, 86, 85, 85, 34, 88, 76, 87, 92, 92, 72

50. A freshmen class of 220 students raised $1200 for a charity. The senior class of 175 students raised $700. What is the average for both groups?


Measures of Central TendencyHome WorkFor questions 51-53, find the mean, median, mode, range, IQR and the standard deviation of each set of data. Then, make a quantitative statement about each data set based on the measures of central tendency. Be sure to include something about the spread of the numbers.

51. Mortgage rates (in percentages): www.mortgagedaily.comYear 1971 1976 1981 1986 1991 1996 2001 2006 2011Rate 7.31% 8.73% 15.58% 9.94% 9.5% 7.92% 7.08% 6.51% 4.84%

52. Golf scores for the British Open top 14. (4 round total)

273 274 277 277 278 278 279

279 280 280 280 280 280 280

53. The number of Facebook friends of 10 students.

45 7 36 12 15 96 150 13 17 20

54. The following is a list of golf scores that a person kept track of over the summer. Find the mean. Would the standard deviation be large or small?74 82 83 81 71 72 71 85 88 72 71 90 71

55. Find the IQR for the list in question 34.

56. Write a list of 10 scores for a test (in percentages) that would have a large standard deviation.

Spiral ReviewSimplify: Work out: Multiply: Simplify:

57. mnp

58. (3x + 1)3 59. (-4r5t6)(-12r-4s-5) 60. √81m6n4 p16


Standard Deviation and Normal DistributionClass Work

61. Create a normal distribution graph for the fast food with the highest calories. Base data is shown below.

** http://www.statisticbrain.com/fast-food-with-the-highest-calories/

62. The average salary for the NHL (National Hockey League) is 1.3 million. If the graph of professional sports’ salaries follows a normal distribution with a mean of 1.56 million and a standard deviation of 1.57, find the z-score of the average NHL salary and then find their percentile pay.

63. What percentile is a 4th grader who scored a 92% on a test that has a mean of 87 and a standard deviation of 2.8.

64. A factory fills lotion bottles with approximately 20 fl. oz. of lotion. The amount of lotion is normally distributed and the factory maintains a standard that at least 99% of the lotion bottles will be filled between 20 and 21 fl. oz. Find the greatest standard deviation that can be allowed. Round to the nearest hundredth.

65. Out of a class of 243, how many students would fall between 1 and 2 standard deviations above the mean? Round to the nearest student.


http://www.statisticbrain.com/fast-food-with-the-highest-calories/

Standard Deviation and Normal DistributionHome Work

66. A class at USA College is very hard. On a test, the average score was 63.25% with a standard deviation of 10.75. If there were 300 students in the class, how many would you expect would get between a 74 and an 85 on the test? Round to the nearest student.

67. Create a normal distribution graph to represent the Mean Annual Salaries of Farming, Fishing and Forestry Occupations. Base data is shown below.

** http://www.statisticbrain.com/farming-and-forestry-occupation-salary-statistics/

68. The average number of photos uploaded on Facebook per day is 250. The data reported has a standard deviation of 100. Find the number of photographs someone with a z-score of 3.5 uploaded in one day.

69. A manufacturing plant makes nickel plates. They put approximately 2 oz. of nickel in each plate. The amount of nickel fluctuates slightly, but the manager guarantees that at least 95% of the plates have between 1.95 and 2.05 oz. of nickel in them. Find the greatest standard deviation that will be allowed to maintain this standard.

70. A 10th grader scores 72% on a standardized test. The mean of the test was 83% and the standard deviation is 3.2. What was the 10th graders reported percentile?

Spiral ReviewSimplify: Factor: Multiply: Simplify:


71.

3m7m2

5

72. 8x3 + 27 73. (x2 + 3x – 1)(2x2 – x – 2) 74. 3√81 r4 s9

Two-Way Frequency TablesClass Work

Put the following information in a two-way frequency table in the space below and use it to answer the questions.

75. At the humane society, during a summer, a total of 625 dogs and cats were brought in to see the veterinarian. Out of those animals, 145 dogs and 15 cats were positive for heartworm. 455 of the animals were dogs, the rest were cats.

a. Find the probability that a dog came in tested positive for heartworm.

b. What percentage of cats did not have heartworm?

c. What is the probability that an animal who tested positive for heartworm was a dog?

d. Find the probability that a cat came in and tested positive for heartworm.

76. At USA University, 300 students were interviewed about the sports that they played. Out of the 300, 170 were girls, the rest were boys. 121 of the girls and 103 of the boys played a sport. The rest did not play any sports.

a. What percentage of girls played a sport?


b. Find the probability that a person who played a sport was a boy.

c. Of the boys, what percentage did not play a sport?

d. Find the probability that a person who did not play a sport was a girl.Two-Way Frequency TablesHome Work


77. At USA College, 1000 students were surveyed about social websites. Half of the college students surveyed were girls. Out of the girls, 460 reported having an account on a social website. Of the boys, 320 stated that they had an account.

a. What is the probability that a person who has a social account is a girl?

b. Find the percentage of boys that do not have an account.

c. Of the girls, what is the probability that they do not have a social account?

d. Given that a person has a social account, what is the probability that they are a boy?

78. A group of students at a university studied leukemia in dogs and cats. 2000 pets participated in their study. 750 were dogs and the rest were cats. 57 of the dogs and 423 cats had leukemia.

a. Did dogs have a greater percentage of leukemia or the cats? Prove your answer mathematically.

b. Of the animals that had leukemia, what percentage were cats?

c. Given that the animal was a dog, what is the probability that it would have leukemia?

d. Find the probability that a dog would not have leukemia.


Spiral ReviewSimplify: (Be careful!) Work out: Multiply: Simplify:

79.

3x

1x−3

80. 3

15∙ 410∙ 25

2481. (3xy5z6)4 82.

4√64m6n20

Sampling and ExperimentsClass Work

83. It was reported that 63% of prison inmates cannot read. A local mayor said that the stat is too low and that it is more like 70%. Develop a simulation with 10 trials and calculate a margin of error for this situation. Does the mayor’s 70% fall within this margin? Prove or disprove his allegation.

84. A 3rd grader guesses 4 answers on a True/False test. Design a simulation to find the probability that the young guesser would get two out of the 4 answers correct. Run your simulation at least 10 times.

85. Soggy Burger is giving out 6 different game cards with each burger purchased. After you collect all 6 cards, you can redeem them for a free burger. Design a simulation and run it 10 times. Come up with a mean number from your data to estimate the number of burgers that you must purchase in order to get a free one.


86. The number of cancer cures in dogs was 15% better using treatment A over treatment B. Create and run a simulation to decide if the number 0 falls in your margin of error. What does the number 0 represent in this situation?

Sampling and ExperimentsHome Work

87. You are bored in class and start flipping a coin with your friend. Heads you win, tails your friend wins. She wins 5 times in a row. Is she somehow cheating? Use a simulation to prove or disprove a claim that she is cheating.

88. Your friend is terrified of flying and claims that 50% of fatalities happen when the plane is descending or landing. In reality, you know that the odds of a plane crashing are 1 in 29.4 million. Despite that, your friend continues to be terrified. Finally, you decide to look up information about plane crashes on the internet and find the actual stat of crashing while descending or landing is 41%. Prove or disprove your friend’s claim of 50% using a simulation.

89. Two different skin creams are being tested on how much they help a person’s skin. Cream A reported that 62% of people had better skin using the cream and Cream B reported 51% of people having improved skin. Is Cream A really better than Cream B? Design a simulation using the difference of the successes of the creams to see if the number of zero (no difference) falls within your margin of error.

90. A student at your school claims that 2/3 of the school plays video games every night. You feel that this stat is way too high. You ask your homeroom of 36 students who plays video games at night. 17 of those students admitted playing every night. Is this a large enough sample to prove the original claim to be incorrect? Develop a simulation to prove or disprove the claim that 2/3 or the school plays video games each night.



91. 2

1x+5 92.

116∙ 815∙ 35

493. (-10xy2z6)3 94.

3√64m6n20

Review: Statistics & Probability

Use the Venn diagram below to answer questions #1-5.

1. The Universe is:a. {rational numbers}b. {-12}c. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}d. {-12, -9, -6, -5, -4, -3, -2, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 16}

2. B∪(A∩C)a. {-12}b. {-12, -9, -6, 3, 6, 9, 12}c. {-12, -9, -6, 3, 9}d. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}

3. A∩(B∪C)a. {3, 9}b. {1, 2, 5, 6, 7, 11, 12, 13}c. {1, 2, 3, 5, 6, 7, 9, 11, 12, 13}d. {-12, -9, -6, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}

4. B∩(A∪C)a. {-12, -6, 3, 9}b. {-12}


c. {-9, -5, -3, 1, 2, 5, 7, 11, 13}d. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 7, 9, 11, 13}

5. B∪ A∪Ca. {-12, -9, -6, -5, -4, -3, -2, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 16}b. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}c. {-12, -9, -6, 3, 9}d. {-12}

6. Find the probability of drawing a black card or a number card that is even out of a normal deck of cards.

a. 38.5%b. 50%c. 69.2%d. 88.5%

7. Calculate the probability of spinning a primary color 3 times using the spinner in the diagram to the right.

a. 6.4%b. 21.6%c. 36%d. 60%

8. A doctor’s office estimates that the probability that a patient will come in for a regular checkup is 0.54. The probability that the patient who comes in for a regular checkup and has a cold is 0.25. Find the probability that the patient has a cold, given that they have come in for a regular checkup.

a. 0.19b. 0.29c. 0.46d. 0.79

9. The letters A, B, C, D, E, F, G, and H can be used to make a 4-letter code. How many codes are possible if no letter is repeated?

a. 1,680b. 4,096c. 6,720d. 40,320

10. When playing poker, each player is dealt 5 cards from a standard deck of 52. A “two pair” is when there are 2 sets of 2 cards that are the same (e.g. 2 tens & 2 nines). What is the probability of getting dealt a “two pair” of any set of cards?

a. 0.06%b. 9.5%c. 19%d. 28.5%

Use the graph of a normal distribution to answer questions 11 and 12.


11. If the mean score on a test was an 80% and the data was normally distributed with a standard deviation of 6.5, a student that scored in the 84th percentile would have gotten which of the following scores?

a. 99b. 93c. 90d. 86

12. Out of 400 students, about how many were between -2.5 and -1.5 standard deviations below the mean? Assume that the test scores were normally distributed.

a. 18b. 24c. 54d. 371

13. Calculate the z score for a mean of 83, a value of 74 and a standard deviation of 6.1.a. 1.04b. 1.48c. -1.48d. -0.82

14. Find the original number if it has a z score of 0.528, a mean of 45.7 and a standard deviation of 3.1.

a. 21.03b. 27.23c. 33.34d. 47.34

Use the two-way frequency table to answer questions 15 and 16.

Opinion of Track & Field Athletes about 2 Throwing Events: Discus and Javelin

Likes Javelin Does not like Javelin TotalLikes Discus 0.394 0.265 0.659Does not like Discus 0.227 0.114 0.341Total 0.621 0.379 1

15. Find the probability that an athlete likes discus given that they did not like javelin.a. 36.5%b. 40.2%c. 59.8%d. 69.9%

16. Find the probability that an athlete likes javelin given that they like discus.a. 36.5%b. 40.2%c. 59.8%


d. 69.9%

17. Draw a Venn diagram to represent the following situation. Then, use your diagram to answer questions 18-19.

The data from a survey of 140 students showed that 37 studied music (A), 103 played a sport (B) and 25 studied music and played a sport. The rest of the 140 students do neither.

a) Find the number of students in each set and then, b) explain what each set means.18. A∩ B 19. (A∪B)


20. Create a two-way frequency table from the following information. Use it to answer questions 21 and 22.

A survey of 1,000 people was taken at a local college about whether or not they actually liked morning classes. Out of the total, 582 were female. From the females, 204 liked morning classes. Out of the males, 117 liked morning classes.

21. Find the probability that out of all the people that did not like morning classes, the person is male.

22. What percentage of the people that like morning classes are female?

Extended Constructed Response - Solve the problem, showing all work. A skin-care company started advertising that 40% of its customers reported that they had better results using their facial cleanser. You work for a rival skin-care company, and your job is to prove the results are incorrect.

23. Create and explain a simulation that would help you prove or disprove the claim that 40% of the facial cleanser users had better results.

24. Execute your simulation 10 times, find the mean and then the margin of error.

25. Determine whether or not the number of 40% is accurate or not. Use your data from the simulation to explain your answer.


Sets - KEYClass Work1. Draw a sample space for the following situations: Each answer may vary.

a. Rolling a set of two dice and multiplying the numbers on each to find an answer.

b. Drawing two marbles out of a bag, with replacement. Out of 20 marbles, 4 are red, 10 are blue and the rest are yellow.

c. Spinning a spinner with the numbers 1 through 8 on it.

2. On the back of this worksheet or on another piece of paper, draw a Venn Diagram that compares the choices of candy between a group of boys and a group of girls on a field trip. Use the following information. The boys and their choices are as follows: Logan chose licorice and toffee, Arik chose gum and Snickers, Jim chose licorice and Snickers, Rob chose toffee and Reese’s and Bill chose gum and mints. The girls and their choices are as follows: Tess chose mints and Skittles, Brianna chose Skittles and Mounds, Paige chose Starburst and Snickers, Katie chose toffee and Snickers and Grace chose Skittles and Starburst.


{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {0, 3, 8, 9, 10, 14}B = {1, 3, 5, 6, 7, 8, 13, 14}C = {3, 4, 5, 6, 12, 14}

{3, 8, 14} {1, 3, 4, 5, 6, 7, 8, 12, 13, 14} {3, 8, 14} {0, 9, 10}

{2, 4, 11, 12, 15} {3, 14} {0, 3, 5, 6, 8, 9, 10, 14} {0, 1, 7, 8, 9, 10, 13}




c. Find: i. A∩B ii. BUC iii. A∩(BUC) iv. ~(BUC)∩A

v. ~(AUB) vi. A∩B∩C vii. AU(B∩C) viii. (AUB)∩~C

4. The following Venn Diagram shows the results of a college survey about extra-curricular activities that men and women do regularly. Use this diagram to list the members of the following sets and then write a sentence to describe the result.a. U

b. A∩B

c. A∩(~B)

d. AUB

e. ~A

f. ~(A∩B)


{walking, aerobics, yoga, eating, sitting}

{hockey, football, soccer, weights, swimming, running, walking, aerobics, yoga, eating, sitting}

{weights, swimming, running}

{hockey, football, soccer}

{hockey, football, soccer, weights, swimming, running, walking, aerobics, yoga}

{walking, aerobics, yoga, hockey, football, soccer, sitting, eating}

SetsHome Work5. Draw a sample space for the following situations: Each answer may vary.

a. Drawing a card from a normal deck of cards. Take only the different suits into consideration.

b. Rolling a single, six-sided die AND then flipping a coin.

c. Flipping a coin AND then spinning a spinner with the numbers 1 through 4 on it.

6. On the back of this worksheet or on another piece of paper, draw a Venn Diagram that represents the following situation. At USA High School, from a survey of 100 people, a student found that 90 had a TV, 40 had a laptop computer and 30 of those same people had both a TV and a laptop.


H – 1/2 T – 1/21 – 1/6 1/12 1/122 – 1/6 1/12 1/123 – 1/6 1/12 1/124 – 1/6 1/12 1/125 – 1/6 1/12 1/126 – 1/6 1/12 1/12

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A = {3, 8, 9, 14, 15}B = {1, 2, 4, 8, 11, 12, 13}C = {2, 3, 5, 6, 7, 11}

{8} {1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 15} {8, 9, 14, 15} {1, 2, 4, 8, 11, 12, 13}

{0,1,4,10,12,13} {3, 8} {Ø} {1, 2, 3, 4, 8, 11, 12, 13}

{swimming, running, sailing, skiing, snowboarding, hiking, fishing, 4-wheeling, biking, hunting}

{skiing, snowboarding, hiking, fishing}

{swimming, running, sailing}

{4-wheeling, biking, hiking}

{swimming, running, sailing, skiing, snowboarding, hiking, fishing, 4-wheeling, biking, hunting}

{swimming, running, sailing, 4-wheeling, biking, hiking}




c. Find: i. A∩B ii. BUC iii. A∩(AUC) iv. ~(A∩C)∩B

v. ~(AUC) vi. A∩(BUC) vii. A∩B∩C viii. BU(A∩C)

8. The following Venn Diagram shows activities that male (A) and female (B) teens in Colorado do on the weekends. Use this diagram to list the members of the following sets and then write a sentence to describe the result.a. U

b. A∩B

c. A∩(~B)

d. AUB

e. ~A

f. ~(A∩B)


6m4n3-2y 13 3

12x(2x2 – 3) x2

IndependentDependent

Overlapping 8/13 or 0.62 or 62%

Mutually exclusive ¾ or o.75 or 75%

0.33 or 33%

0.50 or 50%

0.084 = 0.084, therefore independent

Spiral ReviewSimplify: Simplify: Factor: Simplify:

9. √36m8n6 10. −12x−6 y6

18 x−6 y−7 11. 24x3 – 36x 12.

1x4

1x6

Independence and Conditional ProbabilityClass Work

13. Label the events as dependent or independent:

a. Your family decides to take a trip to Disney World for spring break. Your friend’s family decides to go to Disneyland.

b. You secretly take out all of the Aces from a deck of cards and then get your friend to see how many tries it takes to get an Ace.


a. A = Drawing a red card from a regular deck of cards B = Drawing a face card from a regular deck of cards

b. A = Rolling an odd number on a six-sided die. B = Drawing a spade from a regular deck of cards


a. Find the probability that it is raining, given that it is cold.

b. A bag contains different colored disks that are numbered from 1 to 10. The probability that the disk is green is 0.6. The probability that it is green and odd is 0.3. What is the probability that the disk is odd, given that it is green?



a. Rolling a 10 on a set of six-sided die and then rolling a 5.

b. A = taking math during your senior year at high school B = going to college


0.9 = 0.9, therefore independent

Dependent Dependent

Mutually exclusive 2/5, 0.4 or 40%

Overlapping 29/52, 0.558 or 55.8%

0.67 or 67% 0.6 or 60%

0.875 ≠ 0.95, therefore dependent

Independence and Conditional ProbabilityHome Work

17. Label the events as dependent or independent:

a. The cost of a person’s insurance is high. Looking at the person’s driving record, they have had a lot of accidents.

b. You drink two 40oz. sodas a day for three weeks. In that time, you gain 15 pounds.


a. A bag of 15 marbles has 3 red marbles, 3 blue marbles, 3 yellow marbles, 3 green marbles and 3 black marbles. A = Drawing a red marble B = Drawing a blue marble

b. Using a regular deck of cards: A = Drawing an even numbered card B = Drawing a heart


a. Find the probability that a student is in a band, given that they take a music class.

b. Find the probability that a student gets good grades, given that they play a sport.



a. The probability that a person owns the car they drive, i.e. no payments, in USA High School is 40%. The probability that the person owns their car and knows how to change the oil is 35%. Decide if the events are independent and then find the probability that a person at USA High knows how to change the oil on a car, given that they own the car.

b.


0.6 ≠ 0.8, therefore dependent

(5x – 3y)(25x2 + 15xy + 9y2) (4m – 9)(4m + 9) 2r2p4√6Typeequationhere .

2m n

400 different lunches

80 different televisions

24 different numbers

252 ways/committees

47,174,400 license plates

30 different types of sweaters

1/70

1/7

0.0042%

Spiral ReviewFactor: Factor: Simplify: Simplify:

21. 125x3 – 27y322. 16m2 – 81 23. √24 r4 p8 24.

6n3m

Permutations & CombinationsClass Work25. For lunch, the school cafeteria has a selection of 4 entrees, 5 sides, 5 drinks, and 4 desserts. Assuming that you select one item from each category, how many different lunches could be made?

26. An electronics store is selling new televisions. The different choices include: rear projections, LCD, DLP, CRT, or plasma; full screen or wide screen; 13”, 19”, 27”, 32”, 36”, 41”, 51”, or 63”. How many different televisions does the store have to offer?

27. How many 4 digit numbers can be made using the digits 3, 6, 7, and 8 if the numbers cannot be repeated?

28. In how many ways can you select a committee of 5 students from a pool of 10 students?


30. The manager for a retail store must decide which sweaters to stock for the upcoming fall season. A sweater from one manufacturer comes in 5 different colors and in 3 different textures. The manager decides that the store will that the store will stock the sweater in 3 different colors and 2 different textures. How many different types of sweaters can the store choose to stock up on for the upcoming fall season?

31. A committee of 4 students is to be chosen from a group of 8 students. Barbara, Jack, Anna, and Connor are students in the group. What is the probability that all 4 of them will be chosen for the committee?

32. If the letters in the word LIBERTY are arranged at random, and no repetition is allowed, what is the probability that the first letter is a “T”?


0.0042%

32 different kinds of batteries

72 different breakfasts

720 ways to read the books

43,949,268 ways

59,400 different committees

180,835,200 license plates

1/8

1/15

1/3

33. When playing a game of poker, each player is dealt 5 cards from a standard deck of 52. A flush is when all 5 of the cards are of one suit. There are 4 suits in each deck. What is the probability of getting dealt a flush?

34. A 4 digit number is formed from the numbers 1, 2, 3, 4, 5, 6, and 7, with no repetitions. What is the probability that the number will be between 2,000 and 6,000?

Permutations & CombinationsHomework35. Wal-mart has a selection of batteries that you could purchase. The brands that are offered include EverReady, Duracell, Energizer, or Ray-O-Vac. After selecting the brand, you have to decide whether to get alkaline or non-alkaline batteries. Finally, you must select the size: AAA, AA, C, or D. How many different kinds of batteries are available for you to buy?

36. You wake up in the morning and go to the pantry to look for breakfast. You have a choice of Pop-Tarts, muffins, granola bars, or cereal. To drink, you have a choice of whole milk, 2% milk, skim mil, orange juice, apple juice, and water. Your mother insists that you take a multi-vitamin with your breakfast. You can choose from Flintstones vitamins, One-a-Day vitamins, or Chock’s Vitamins. How many different breakfasts made up of an entree, drink and vitamin could you make?

37. At the beginning of the summer, you have 6 books to read. In how many ways can you read the 6 books?

38. Five students from the 90 students in your class not running for class president will be selected to count the ballots to determine who wins the presidential race. In how many ways can the 5 students be selected?

39. A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committees can be formed from this group?


41. If the letters in the word HEPTAGON are arranged at random, and no repetition is allowed, what is the probability that the first letter is a “P”?

42. A committee of 4 students is to be chosen from a group of 6 students. Mike, Billy, Kendra, and Sarah are students in the group. What is the probability that all 4 of them will be chosen for the committee?


43. A 4 digit number is formed from the numbers 1, 2, 3, 4, 5, and 6 with no repetitions. What is the probability that the number will be between 1,000 and 3,000?

44. When playing a game of poker, each player is dealt 5 cards from a standard deck of 52. A pair is when 2 cards are the same. What is the probability of getting dealt a pair of any card?


Mean = 77.8Median = 75.5Mode = 75Range = 54IQR = 13Standard Deviation = 14.32**Answers may vary slightly

Mean = 87.138Median = 87.355Mode = noneRange = 3.38IQR = 1.74Standard Deviation = 1.108**Answers may vary slightly

Mean = 343.38Median = 342.925Mode = noneRange = 118.8IQR = 45Standard Deviation = 31.56**Answers may vary slightly

86.3

34

$950

Measures of Central TendencyClass Work

For questions 45-47, find the mean, median, mode, range, IQR and the standard deviation of each set of data. Then, make a quantitative statement about each data set based on the measures of central tendency. Be sure to include something about the spread of the numbers.

45. Test scores for a physics exam: (in percentages)96 43 88 97 75 75 76 75 78 75

46. Top ten time results for a Men’s Giant Slalom race: (in seconds)85.18 85.38 86.48 87.04 87.31 87.40 87.43 88.22 88.38 88.56

47. Women’s Spring Board Diving Results: (total points) 414 379.20 362.40 362.20 345.65 343.00342.85 332.10 317.80 316.80 309.40 295.20

48. The table below shows a frequency of test scores on a math test. Find the mean.

49. Which number would you remove from the list below to get a smaller standard deviation?78, 78, 90, 99, 77, 86, 85, 85, 34, 88, 76, 87, 92, 92, 72

50. A freshmen class of 220 students raised $1200 for a charity. The senior class of 175 students raised $700. What is the average for both groups?


Mean = 8.6Median = 7.92Mode = noneRange = 10.74IQR = 2.925Standard Deviation = 2.87**Answers may vary slightly

Mean = 278.21Median = 279Mode = 280Range = 7IQR = 3Standard Deviation = 2.21**Answers may vary slightly

Mean = 41.1Median = 18.5Mode = noneRange = 143IQR = 32Standard Deviation = 44.07**Answers may vary slightly

77.77

13

Answers will vary. Look for a large range.

9m3n2p8

Measures of Central TendencyHome Work

For questions 51-53, find the mean, median, mode, range, IQR and the standard deviation of each set of data. Then, make a quantitative statement about each data set based on the measures of central tendency. Be sure to include something about the spread of the numbers.

51. Mortgage rates (in percentages): www.mortgagedaily.comYear 1971 1976 1981 1986 1991 1996 2001 2006 2011Rate 7.31% 8.73% 15.58% 9.94% 9.5% 7.92% 7.08% 6.51% 4.84%

52. Golf scores for the British Open top 14. (4 round total)

273 274 277 277 278 278 279

279 280 280 280 280 280 280

53. The number of Facebook friends of 10 students.

45 7 36 12 15 96 150 13 17 20

54. The following is a list of golf scores that a person kept track of over the summer. Find the mean. Would the standard deviation be large or small?74 82 83 81 71 72 71 85 88 72 71 90 71

55. Find the IQR for the list in question 34.

56. Write a list of 10 scores for a test (in percentages) that would have a large standard deviation.

Spiral ReviewSimplify: Work out: Multiply: Simplify:


mnp 27x3 + 27x2 + 9x + 1 48rt 6

s5

z-score = -0.17, 43rd percentile

z-score = 1.79, 96th percentile

σ = 0.17 oz.

57. mnp

58. (3x + 1)3 59. (-4r5t6)(-12r-4s-5) 60. √81m6n4 p16

Standard Deviation and Normal DistributionClass Work

61. Create a normal distribution graph for the fast food with the highest calories. Base data is shown below.

** http://www.statisticbrain.com/fast-food-with-the-highest-calories/

62. The average salary for the NHL (National Hockey League) is 1.3 million. If the graph of professional sports’ salaries follows a normal distribution with a mean of 1.56 million and a standard deviation of 1.57, find the z-score of the average NHL salary and then find their percentile pay.

63. What percentile is a 4th grader who scored a 92% on a test that has a mean of 87 and a standard deviation of 2.8.

64. A factory fills lotion bottles with approximately 20 fl. oz. of lotion. The amount of lotion is normally distributed and the factory maintains a standard that at least 99% of the lotion bottles will be filled between 20 and 21 fl. oz. Find the greatest standard deviation that can be allowed. Round to the nearest hundredth.


http://www.statisticbrain.com/fast-food-with-the-highest-calories/

33 students

41 students

600 photos

σ = 0.05 ounces

<1 percentile

24x4 + 5x3 – 7x2 – 5x + 2 3 r s3 3√3 r

65. Out of a class of 243, how many students would fall between 1 and 2 standard deviations above the mean? Round to the nearest student.

Standard Deviation and Normal DistributionHome Work

66. A class at USA College is very hard. On a test, the average score was 63.25% with a standard deviation of 10.75. If there were 300 students in the class, how many would you expect would get between a 74 and an 85 on the test? Round to the nearest student.

67. Create a normal distribution graph to represent the Mean Annual Salaries of Farming, Fishing and Forestry Occupations. Base data is shown below.

** http://www.statisticbrain.com/farming-and-forestry-occupation-salary-statistics/

68. The average number of photos uploaded on Facebook per day is 250. The data reported has a standard deviation of 100. Find the number of photographs someone with a z-score of 3.5 uploaded in one day.

69. A manufacturing plant makes nickel plates. They put approximately 2 oz. of nickel in each plate. The amount of nickel fluctuates slightly, but the manager guarantees that at least 95% of the plates have between 1.95 and 2.05 oz. of nickel in them. Find the greatest standard deviation that will be allowed to maintain this standard.

70. A 10th grader scores 72% on a standardized test. The mean of the test was 83% and the standard deviation is 3.2. What was the 10th graders reported percentile?

Spiral Review


157m

(2x + 3)(4x2 – 6x + 9)

Positive for heartworm Negative for heartworm Total

Dogs 0.232 0.496 0.728

Cats 0.024 0.248 0.272

Total 0.256 0.744 1

0.318 or 31.8%

91%

91%

0.089 or 8.9%

Plays a sport Does not play a sport Total

Girls 0.403 0.163 0.567

Boys 0.343 0.09 0.433

Total 0.746 0.253 1

71%

0.46 or 46%

Simplify: Factor: Multiply: Simplify:

71.

3m7m2

5

72. 8x3 + 27 73. (x2 + 3x – 1)(2x2 – x – 2) 74. 3√81 r4 s9

Two-Way Frequency TablesClass Work


75. At the humane society, during a summer, a total of 625 dogs and cats were brought in to see the veterinarian. Out of those animals, 145 dogs and 15 cats were positive for heartworm. 455 of the animals were dogs, the rest were cats.

a. Find the probability that a dog came in tested positive for heartworm.

b. What percentage of cats did not have heartworm?

c. What is the probability that an animal who tested positive for heartworm was a dog?

d. Find the probability that a cat came in and tested positive for heartworm.

76. At USA University, 300 students were interviewed about the sports that they played. Out of the 300, 170 were girls, the rest were boys. 121 of the girls and 103 of the boys played a sport. The rest did not play any sports.

a. What percentage of girls played a sport?

b. Find the probability that a person who played a sport was a boy.


21%

0.637 or 64%

Account on social website No account on social website Total

Girls 0.46 0.04 0.5

Boys 0.32 0.18 0.5

Total 0.78 0.22 1

0.59 or 59%

36%

0.08 or 8%

0.41 or 41%

Positive for leukemia Negative for leukemia Total

Dogs 0.0285 0.3465 0.375

Cats 0.2115 0.4135 0.625

Total 0.24 0.76 1

The cats are more likely to be diagnosed with leukemia. Make sure students use data from their table to justify answers.

88%

0.076 or 7.6%

0.924 or 92.4%

c. Of the boys, what percentage did not play a sport?

d. Find the probability that a person who did not play a sport was a girl.

Two-Way Frequency TablesHome Work


77. At USA College, 1000 students were surveyed about social websites. Half of the college students surveyed were girls. Out of the girls, 460 reported having an account on a social website. Of the boys, 320 stated that they had an account.

a. What is the probability that a person who has a social account is a girl?

b. Find the percentage of boys that do not have an account.

c. Of the girls, what is the probability that they do not have a social account?

d. Given that a person has a social account, what is the probability that they are a boy?

78. A group of students at a university studied leukemia in dogs and cats. 2000 pets participated in their study. 750 were dogs and the rest were cats. 57 of the dogs and 423 cats had leukemia.

a. Did dogs have a greater percentage of leukemia or the cats? Prove your answer mathematically.

b. Of the animals that had leukemia, what percentage were cats?

c. Given that the animal was a dog, what is the probability that it would have leukemia?

d. Find the probability that a dog would not have leukemia.


31−3 x

112

81x4y20z24 2mn5 4√4m2

Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent 63% of the prison population that cannot read as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the mean and margin of error correctly. Correct answers should include a comparison of their results to the 63% as well as a determination of whether the number falls within their margin of error.

Answers will vary. Look for thorough explanation that includes assigns appropriate values to True and False. Make sure students did the simulation 10 times and generated the mean and margin of error correctly. Correct answers should include probability.

Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent different game cards as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the mean and IQR correctly. Correct answers should include a comparison of their results as well as a determination of a range of possibilities.


79.

3x

1x−3

80. 3

15∙ 410∙ 25

2481. (3xy5z6)4 82.

4√64m6n20

Sampling and ExperimentsClass Work

83. It was reported that 63% of prison inmates cannot read. A local mayor said that the stat is too low and that it is more like 70%. Develop a simulation with 10 trials and calculate a margin of error for this situation. Does the mayor’s 70% fall within this margin? Prove or disprove his allegation.

84. A 3rd grader guesses 4 answers on a True/False test. Design a simulation to find the probability that the young guesser would get two out of the 4 answers correct. Run your simulation at least 10 times.

85. Soggy Burger is giving out 6 different game cards with each burger purchased. After you collect all 6 cards, you can redeem them for a free burger. Design a simulation and run it 10 times. Come up with a mean number from your data to estimate the number of burgers that you must purchase in order to get a free one.


Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent the percentage of the difference between the trials as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the margin of error correctly. Correct answers should include a comparison of their results as well as a determination of whether the number falls within their margin of error.

Answers will vary. Students’ answers will depend on their simulations. Look for a thorough explanation that includes references to their data.

Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent 41% of crashes as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the mean and margin of error correctly. Correct answers should include a comparison of their results to the 50% as well as a determination of whether the number falls within their margin of error.

Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent the percentages for each skin cream as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the mean and margin of error correctly. Correct answers should include a comparison of their results as well as a determination of whether the number falls within their margin of error.

Answers will vary. Look for thorough explanation that includes assigning numbers which appropriately represent 17 of the 36 students that played video games as well as having the design of the simulation being able to randomly generate results. Make sure students did the simulation 10 times and generated the mean and margin of error correctly. Correct answers should include a comparison of their results to the 67% as well as a determination of whether the number falls within their margin of error.

86. The number of cancer cures in dogs was 15% better using treatment A over treatment B. Create and run a simulation to decide if the number 0 falls in your margin of error. What does the number 0 represent in this situation?

Sampling and ExperimentsHome Work87. You are bored in class and start flipping a coin with your friend. Heads you win, tails your friend wins. She wins 5 times in a row. Is she somehow cheating? Use a simulation to prove or disprove a claim that she is cheating.

88. Your friend is terrified of flying and claims that 50% of fatalities happen when the plane is descending or landing. In reality, you know that the odds of a plane crashing are 1 in 29.4 million. Despite that, your friend continues to be terrified. Finally, you decide to look up information about plane crashes on the internet and find the actual stat of crashing while descending or landing is 41%. Prove or disprove your friend’s claim of 50% using a simulation.

89. Two different skin creams are being tested on how much they help a person’s skin. Cream A reported that 62% of people had better skin using the cream and Cream B reported 51% of people having improved skin. Is Cream A really better than Cream B? Design a simulation using the difference of the successes of the creams to see if the number of zero (no difference) falls within your margin of error.

90. A student at your school claims that 2/3 of the school plays video games every night. You feel that this stat is way too high. You ask your homeroom of 36 students who plays video games at night. 17 of those students admitted playing every night. Is this a large enough sample to prove the original claim to be incorrect? Develop a simulation to prove or disprove the claim that 2/3 or the school plays video games each night.


2 x1+5x

724

-1000x3y6z184m2n6 3√4 n2


91. 2

1x+5 92.

116∙ 815∙ 35

493. (-10xy2z6)3 94.

3√64m6n20

Review: Probability & Statistics - Key

Use the Venn diagram below to answer questions #1-5.

1. The Universe is:a. {rational numbers}b. {-12}c. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}d. {-12, -9, -6, -5, -4, -3, -2, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 16}

2. B∪(A∩C)a. {-12}b. {-12, -9, -6, 3, 6, 9, 12}c. {-12, -9, -6, 3, 9}d. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}

3. A∩(B∪C)a. {3, 9}b. {1, 2, 5, 6, 7, 11, 12, 13}c. {1, 2, 3, 5, 6, 7, 9, 11, 12, 13}d. {-12, -9, -6, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}

4. B∩(A∪C)a. {-12, -6, 3, 9}b. {-12}


c. {-9, -5, -3, 1, 2, 5, 7, 11, 13}d. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 7, 9, 11, 13}

5. B∪ A∪Ca. {-12, -9, -6, -5, -4, -3, -2, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 16}b. {-12, -9, -6, -5, -3, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13}c. {-12, -9, -6, 3, 9}d. {-12}

6. Find the probability of drawing a black card or a number card that is even out of a normal deck of cards.

a. 38.5%b. 50%c. 69.2%d. 88.5%

7. Calculate the probability of spinning a primary color 3 times using the spinner in the diagram to the right.

a. 6.4%b. 21.6%c. 36%d. 60%

8. A doctor’s office estimates that the probability that a patient will come in for a regular checkup is 0.54. The probability that the patient who comes in for a regular checkup and has a cold is 0.25. Find the probability that the patient has a cold, given that they have come in for a regular checkup.

a. 0.19b. 0.29c. 0.46d. 0.79

9. The letters A, B, C, D, E, F, G, and H can be used to make a 4-letter code. How many codes are possible if no letter is repeated?

a. 1,680b. 4,096c. 6,720d. 40,320

10. When playing poker, each player is dealt 5 cards from a standard deck of 52. A “two pair” is when there are 2 sets of 2 cards that are the same (e.g. 2 tens & 2 nines). What is the probability of getting dealt a “two pair” of any set of cards?

a. 0.06%b. 9.5%c. 19%d. 28.5%

Use the graph of a normal distribution to answer questions 11 and 12.


11. If the mean score on a test was an 80% and the data was normally distributed with a standard deviation of 6.5, a student that scored in the 84th percentile would have gotten which of the following scores?

a. 99b. 93c. 90d. 86

12. Out of 400 students, about how many were between -2.5 and -1.5 standard deviations below the mean? Assume that the test scores were normally distributed.

a. 18b. 24c. 54d. 371

13. Calculate the z score for a mean of 83, a value of 74 and a standard deviation of 6.1.a. 1.04b. 1.48c. -1.48d. -0.82

14. Find the original number if it has a z score of 0.528, a mean of 45.7 and a standard deviation of 3.1.

a. 21.03b. 27.23c. 33.34d. 47.34

Use the two-way frequency table to answer questions 15 and 16.

Opinion of Track & Field Athletes about 2 Throwing Events: Discus and Javelin

Likes Javelin Does not like Javelin TotalLikes Discus 0.394 0.265 0.659Does not like Discus 0.227 0.114 0.341Total 0.621 0.379 1

15. Find the probability that an athlete likes discus given that they did not like javelin.a. 36.5%b. 40.2%c. 59.8%d. 69.9%

16. Find the probability that an athlete likes javelin given that they like discus.a. 36.5%b. 40.2%c. 59.8%


d. 69.9%

17. Draw a Venn diagram to represent the following situation. Then, use your diagram to answer questions 18-19.

The data from a survey of 140 students showed that 37 studied music (A), 103 played a sport (B) and 25 studied music and played a sport. The rest of the 140 students do neither.

a) Find the number of students in each set and then, b) explain what each set means.18. A∩ B 19. (A∪B)


a) 12b) The students that study

music but do NOT play sports

a) 25b) The students that neither

study music nor play sports

20. Create a two-way frequency table from the following information. Use it to answer questions 21 and 22.

A survey of 1,000 people was taken at a local college about whether or not they actually liked morning classes. Out of the total, 582 were female. From the females, 204 liked morning classes. Out of the males, 117 liked morning classes.

Likes morning classes Does not like morning classes Total

Male 0.117 0.301 0.418Female 0.204 0.378 0.582Total 0.321 0.679 1

21. Find the probability that out of all the people that did not like morning classes, the person is male.

22. What percentage of the people that like morning classes are female?

Extended Constructed Response - Solve the problem, showing all work. A skin-care company started advertising that 40% of its customers reported that they had better results using their facial cleanser. You work for a rival skin-care company, and your job is to prove the results are incorrect.

23. Create and explain a simulation that would help you prove or disprove the claim that 40% of the facial cleanser users had better results.

24. Execute your simulation 10 times, find the mean and then the margin of error.

25. Determine whether or not the number of 40% is accurate or not. Use your data from the simulation to explain your answer.


0.443 or 44.3%

0.636 or 63.6%

Answers will vary. Look for a though explanation that includes assigning numbers which appropriately represent 40% reporting “yes” as well as having the design of the simulation being able to randomly generate results.

Answers will vary. Make sure that the students did the simulation 10 times and generated the mean and margin of error correctly.

Answers will vary. Correct answers should include a comparison of their results to the 40% as well as a determination of whether the number falls within their margin of error.

content.njctl.orgcontent.njctl.org/.../probability-cw-and-hw-2016-01-05.d… · Web view32. If...

Documents

Transcript of content.njctl.orgcontent.njctl.org/.../probability-cw-and-hw-2016-01-05.d… · Web view32. If...