Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U. S. residents and 40 Australians is obtained. Consider the random variables described below: X: the number of US residents (out of 50) with blood type AB. Y: the number of Australians (out of 40) with blood type AB. Z: the total number of individuals (out of 90) with blood type AB. Which of the following is true about the random variables X, Y, and Z? Check all that apply.

X is a binomial random variable with n = 50 and p = 0.04

Y is a binomial random variable with n = 40 and p = 0.015

Z is a binomial random variable with n = 90 and p = 0.055

Question

Mathematics

Iris Goodwin

21 August, 13:23

Blood type AB is the rarest blood type, occurring in only 4% of the population in the United States. In Australia, only 1.5% of the population has blood type AB. Suppose a random sample of 50 U. S. residents and 40 Australians is obtained. Consider the random variables described below: X: the number of US residents (out of 50) with blood type AB. Y: the number of Australians (out of 40) with blood type AB. Z: the total number of individuals (out of 90) with blood type AB. Which of the following is true about the random variables X, Y, and Z? Check all that apply.

X is a binomial random variable with n = 50 and p = 0.04

Y is a binomial random variable with n = 40 and p = 0.015

Z is a binomial random variable with n = 90 and p = 0.055

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Answers (1)

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Cohen · Answer 1

Given details are:

X : the number of US residents (out of 50) with blood type AB.

Y : the number of Australians (out of 40) with blood type AB.

Z : the total number of individuals (out of 90) with blood type AB.

Following are true:

X is a binomial random variable with n = 50 and p = 0.04

Y is a binomial random variable with n = 40 and p = 0.015

Explanation:

The sentences for X and Y are true. The sentence for Z is not true because Z=X+Y and X and Y do not have same probabilities.