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Assignment 5
Assignment 5
4.46(a)
Age
18-2526-40Total
GoalsGetting Rich405310715
Other95190285
Total5005001000
(b)Simple event: Has a goal of getting rich.
Joint event: Has a goal of getting rich and is between 18-25 years old.
(c)P(Has a goal of getting rich) = 715/1000 = 0.715
(d)P(Has a goal of getting rich and is in the 26-40 year old group) = 310/1000 = 0.31
(e)P(Has a goal of getting rich | in the 26-40 year old group) = 310/500 = 0.62
Since P(Has a goal of getting rich | in the 26-40 year old group) P(Has a goal of getting rich), the events age group and has getting rich as a goal are not statistically independent.4.49P(engage) = .13, P(not engage) = .67, P(actively disengaged) = .20
P(strongly agreed | engaged) = .48, P(strongly agreed | not engaged) = .20, P(strongly agreed | actively disengaged) = .03
P(engaged | strongly agree) = (.48*.13)/(.48*.13 + .20*.67 + .03*.20) = 0.30834.51
P(HIV is present | ELISA has given a positive result )
= (0.995)(0.015)/((0.995)(0.015)+(0.01)(0.985) = 0.6024
5.1(a)Distribution A
Distribution B
cont.
XP(X)X*P(X)XP(X)X*P(X)00.500.0000.050.00
10.200.2010.100.10
20.150.3020.150.30
30.100.3030.200.60
40.050.2040.502.00
1.001.00
1.003.00
= 1.00
= 3.00
(b) Distribution A
X(X
)2P(X)(X
)2*P(X)
0(1)20.500.50
1(0)20.200.00
2(1)20.150.15
3(2)20.100.40
4(3)20.050.45
2=1.50
= 1.22
(b)
Distribution B
X(X
)2P(X)(X
)2*P(X)
0(3)20.050.45
1(2)20.100.40
2(1)20.150.15
3(0)20.200.00
4(1)20.500.50
2=1.50
= 1.22
(c)Distribution A: Because the mean of 1 is greater than the median of 0, the distribution is right-skewed.
Distribution B: Because the mean of 3 is less than the median of 4, the distribution is left-skewed.
The means are different but the variances are the same.
5.3(a)Based on the fact that the odds of winning are expressed out with a base of 31,478, you will think that the automobile dealership sent out 31,478 fliers.
(b)
= $ 5.49
(c)
= $ 84.56
(d)The total cost of the prizes is $15,000 + $500 + 31,476 * $5 = $172,880. Assuming that the cost of producing the fliers is negligible, the cost of reaching a single customer is $172,880/31478 = $5.49. The effectiveness of the promotion will depend on how many customers will show up in the show room.5.6PHStat output:
Probabilities & Outcomes:PX
0.1250
0.2403851
0.3076922
0.1634623
0.0865384
0.0576925
0.0096156
0.0096157
Statistics
E(X)2.105769
Variance(X)2.152274
Standard Deviation(X)1.467063
(a)E(X) = 2.1058
(b)
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