Checkpoint- Random variables

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

A. X is a binomial random variable with n = 50 and p = 0.04 B. Y is a binomial random variable with n = 40 and p = 0.015

In Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on parole. Assume that whether or not one prisoner returns to prison is independent of whether any of the others return to prison. Let the random variable X be the number of parolees out of 15 that return to prison within 3 years. What is the value of the parameter n for the binomial random variable X?

N=15

Colorblindness is any abnormality of the color vision system that causes a person to see colors differently than most people, or to have difficulty distinguishing among certain colors (www.visionrx.com). Colorblindness is gender-based, while the majority of sufferers being males. Roughly 8% of white males have some form of colorblindness, while the incidence among white females is only 1%. A random sample of 20 white males and 40 white females was chosen. Let X be the number of males (out of the 20) who are colorblind. Let Y be the number of females (out of the 40) who are colorblind. Let Z be the total number of colorblind individuals in the sample (males and females together). What is the probability that exactly 2 of the 20 males are colorblind? (Note: Some answers are rounded.) 0.08 0.2711 0.0519 0.5422 0.0159

P(X=2)=0.2711 n=20 p=0.08 x=2

In Texas, 30% of parolees from prison return to prison within 3 years. Suppose 15 prisoners are released from a Texas prison on parole. Assume that whether or not one prisoner returns to prison is independent of whether any of the others return to prison. Let the random variable X be the number of parolees out of 15 that return to prison within 3 years. What is the value of the parameter p for the binomial random variable X? Round your value for p to two decimal places, if needed.

P=0.30

In the following random experiment, decide whether the random variable X is binomial or not: Approximately 1 in 10 people are left-handed. Let X be the number of people that are left-handed out of a random sample of 200 individuals. Although the individuals are sampled without replacement, it is assumed that we are sampling from such a vast population that the selections are virtually independent.

Yes the random variable is a binomial because the trials are independent