Assignment

Q1Find the parameters of binomial distribution when mean=4 and variance=3.

Q2. The output of a production process is 10% defective. What is the probability of selecting exactly two defectives in a sample of 5?

Q3. It is observed that 80% of television viewers watch “Boogie-Woogie” Programme. What is the probability that at least 80% of the viewers in a random sample of five watch this Programme?

Q4. The normal rate of infection of a certain disease in animals is known to be 25%.In an experiment with 6 animals injected with a new vaccine it was observed that none of the animals caught the infection. Calculate the probability of observed result.

Q5. If on average 8 ships out of 10 arrive safely at a port, find the mean and standard deviation of the number of ships arriving safely out of a total of 1600 ships.

Q6. Eight coins are thrown simultaneously. Find the chance if throwing(i) At least 6 heads.(ii) No heads and(iii) All heads(iv)

Q7. In a town 10 accidents took place in a span of 50 days. Assuming that the number of accidents per day follows the Poisson distribution, find the probability that there will be three or more accidents in a day.

Q8. The distribution of typing mistakes committed by a typist is given below. Assuming a Poisson mode, find out the expected frequencies-

No. of mistakes per page

0 1 2 3 4 5

No. of pages

142 156 69 27 5 1

Q9. Find the probability that the value of an item drawn at random from a normal distribution with mean 20 and standard deviation 10 will be between:

(i) 10 and 15(ii) –5 and 10(iii) 15 and 25

Q10. A brokerage survey reports that 30% of individual investors have used a discount broker, i.e. one which does not charge the full commission. In a random sample of 9 individuals, what is the probability that

(i) exactly two of the sampled individuals have used a discount broker?(ii) Not more than three have used a discount broker?

(iii) At least three of them have used a discount broker?

Q11. Find the probability that in a family of 5 children there will be(i) at least one boy (ii) at least one boy and one girl(assume that the probability of a female birth is 0.5)

Q.12 Find p for a binomial variable X, if n=6 and 9P(X=4)=P (X=2).

Q13. The lifetimes of certain kinds of electronic devices have a mean of 300 hours and standard deviation of 25 hours. Assuming that the distribution of these lifetimes which are measured to the nearest hour, can be approximated with a normal curve

(a) Find the probability that any one of these electronic devices will have a lifetime of more than 350 hours.

(b) What percentage will have lifetimes of 300 hrs or less?(c) What percentage will have lifetimes from 220 to 260 hours?

Q14. Five fair coins were tossed 100 times. From the following outcomes, calculate expected frequencies-

No. of heads up

0 1 2 3 4 5

Observed frequency

2 10 24 35 18 8

Q15. A factory produces blades in packets of 10.The probability of a blade is to be defective is 0.2 percent. Find the number of packets having two defective blades in a consignment of 10,000 packets.

Q16. If the standard deviation of a Poisson variable is square root of 2 then find the probability that x is strictly positive?

Q17. A normal curve has a mean of 20 and standard deviation of 10. find the area between x1= 15 and x2= 40.

Q18. In a certain examination the percentage of passes and distinction were 46 and 9 respectively. Estimate the average marks obtained by the candidates, the minimum pass and distinction marks are 40 and 75 respectively (Assume the distribution of marks to be normal)

Q19. The number of accidents ion a year attributed to taxi drivers in a city follows Poisson distribution with mean 3. Out of 1000 taxi drivers find approximately the number of drivers with

(i) no accidents in a year.(ii) More than 3 accidents in a year.

Q20. The average absentee rate in economics lecture sections is historically 15%. In a section of 200 students:

(a) What is the probability that on a given day 160 or more students will attend class?

(b) What is the probability that 180 or fewer students will attend?(c) What is the probability that between 165 and 185 students will attend?

Q21. How would you use the normal distribution to find approximately the frequency of exactly 5 successes in 100 trials, the probability of success in each trial being p=0.1

Q22. In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution.

Q23. 1000 light bulbs with a mean life of 120 days are installed in a new factory and their length of life is normally distributed with standard deviation of 20 days.

(d) How many bulbs will expire in less than 90 days?(e) If it is decided to replace all the bulbs together, what interval should be

allowed between replacements if not more than 10% should expire before replacement?

Q24. The income of a group of 10,000 persons was found to be normally distributed with mean Rs 1750 per month and standard deviation is Rs 50. Show that this group 95% had income exceeding Rs 16568 and only 5% had income exceeding Rs 1832. What was the lowest income among the richest 100.

Q25. A sample of 100 items is taken at random from a batch known to contain 40% defectives. What is the probability that the sample contains-(i)at least 44 defectives (ii) exactly 44 defectives