Question

Color-blindness 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). Color-blindness is gender-based, with 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 color-blind. Let Y be the number of females (out of the 40) who are color-blind. Let Z be the total number of color-blind individuals in the sample (males and females together). Which of the following is true about the random variables X, Y, and Z? X is binomial with n = 20 and p = .08. Y is binomial with n = 40 and p = .01. Z is not binomial. All of the above are true. Only (A) and (B) are true.

Answer 1

Answer: c) All of the above

Step-by-step explanation:

a) X=the number of color-blind males of the randomly chosen 20 individuals

Thus, X is binomial with n = 20 and p = 0.08.

Y represents the number of color-blind females of the randomly chosen 40 individuals

Thus, Y is also binomial with n = 40 and p = 0.01.

b) However, Z represents the total number of color-blind  which is 60. The probability of being color-blind is not equal among all individuals as it is for X (0.08) and Y (0.09). Thus, Z is not binomial.

In conclusion both a and b are correct, which gives the correct answer number c) all of the above.