Multiple Choice 1. Suppose that 34% of the population has mood swings, allergies

Question

Multiple Choice

1. Suppose that 34% of the population has mood swings, allergies, irritability and depression (MAID) and is known to consume dairy products. Also, 80% of the populace consumes dairy products. It is also known that 70 % of the population either consumes dairy products or has MAID. What is the probability that a randomly chosen person has MAID?

Select one:

a. 0.240

b. 0.272

c. 0.440

d. 0.560

2.The number of people getting sick from imported meat products in a certain city in one month was found to be normally distributed with mean and standard deviation :XN(U=190, =22).What is the probability that the number sick next month in that city would be greater than 160?

Select one:

a. 0.0869

b. 0.4131

c. 0.5869

d. 0.9131

3.Random variable X has cost function 3X + 600. The expected value of X is 20 and the variance of X is 4. What is true about the cost function (expected value and variance)?

Select one:

a. E[3X + 600] = 660                 E[3X + 600] = 36

b. E[3X + 600] = 60                   E[3X + 600] = 636

c. E[3X + 600] = 660                 E[3X + 600] = 12

d. E[3X + 600] = 660                 E[3X + 600] = 636

4.Random variable X has mean X = 24 and standard deviation X = 6.   Random variable Y has mean Y = 14 and standard deviation Y = 4.   A new random variable Z was formed, where Z = X + Y. What can we conclude about X, Y, and Z with certainty? That is, which one is true?

Select one:

a. Z = 38            Z = 6                          X and Y are related

b. Z = 38            Z = 7.211                   X and Y are independent

c. Z = 38            Z = unknown             X and Y are independent

d. Z = 38            Z = 10                        X and Y are mutually exclusive

Explanation / Answer

Question1

Pr(MAID and consume dairy products) = 0.34 = Pr(A B)

Pr(consume dairy products) = 0.80 = Pr(A)

Pr(Consume dairy products or has MAID) = 0.70 = Pr(A U B)

Pr(MAID = Pr(B)

Pr(A U B) = Pr(A) + Pr(B) - Pr(A   B)

0.70 = 0.80 + Pr(B) - 0.34

Pr(B) = 0.70 + 0.34 - 0.80 = 0.24

Option A is correct.

Question 2

Pr(X > 160) = 1 - Pr(x < 160 ; 190 ; 22)

Z = (160 - 190)/22 = -1.3636

Pr(X > 160) = 1 - Pr(x < 160 ; 190 ; 22) = 1 - Pr(Z < -1.3636) = 1 - 0.0863 = 0.9131

option d is right

Question 3

E[3X + 600] = 3 E(X) = 3 * 20 + 600= 660

Var(3X + 600) = Var(3X) = 9 * var(X) = 9 * 4 = 36

Option A is correct.

Question 4

Z = 24 + 14 = 38

Z = sqrt [X2 + Y2] = sqrt [62 + 42] = 7.2111

X are Y are independent.

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