Question

A particular variable measured on the US population is approximately normally distributed with a mean of 126 and a standard deviation of 20. Consider the sampling distribution of the sample mean for samples of size 36. Enter answers rounded to three decimal places.

According to the empirical rule, in 95 percent of samples the SAMPLE MEAN will be between the lower-bound of ____and the upper-bound of_____

For a particular large group of people, blood types are distributed as shown below. (Note that each person is classified as having exactly one of these blood types.)

Blood Type	O	A	B	AB
Probability	0.2	0.44	0.11	0.25

(a) If one person is selected at random, what is the probability that the selected person's blood type will be either AB or O?

A. 0.45
B. 0.4
C. 0.05
D. None of the above.

(b) A person who has type B blood can safely receive blood transfusions from people whose blood type is either O or B. If a person is selected at random, what is the probability that the selected person will be able to safely donate blood to a person with type B blood?

A. 0.55
B. 0.31
C. 0.11
D. None of the above.

(c) If two people are independently selected at random, what is the probability that both will have type O blood?

A. 0.04
B. 0.4
C. 0.2
D. None of the above.

Answer 1

Given,

µ = 126

σ = 20

n = 36

σ_{x̅ =} σ/sqrt(n) = 20/sqrt(36) = 20/6 = 10/3

According to 95% Empirical Rule, in case of normal distribution 95% of data will fall within 2 standard deviations.

Lower Bound = µ - 2*σ_x̅ = 126 - 2*(10/3) = 119.33

Upper Bound = µ + 2*σ_x̅ = 126 + 2*(10/3) = 132.67

According to the empirical rule, in 95 percent of samples the SAMPLE MEAN will be between the lower-bound of 119.33 and the upper-bound of 132.67

Answer a)

P(AB or O) = P(AB) + P(O) - P(AB AND O)

P(AB or O) = 0.25 + 0.20 - 0 [P(AB AND O) = 0 because two events are mutually exclusive]

P(AB or O) = 0.45 (Option A)

Answer b)

P(O or B) = P(O) + P(B) - P(O AND B)

P(O or B) = 0.2 + 0.11 - 0 [P(O AND B) = 0 because two events are mutually exclusive]

P(O or B) = 0.31 (Option B)

Answer c)

P(Two selected people have Type O Blood) = P(O)*P(O) [Because two events are independent]

P(Two selected people have Type O Blood) = 0.2*0.2

P(Two selected people have Type O Blood) = 0.04 (Option A)