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)

_966170961.unknown

_966171059.unknown

_1223648689.unknown

_1288514059.unknown

_1223648674.unknown

_966171025.unknown

_966171054.unknown

_966171009.unknown

_953453762.unknown

_953453805.unknown

_953453501.unknown

_953453503.unknown

_953451270.unknown