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. Color-blindness is gender-based, with the majority of sufferers being males. Roughly 8% of white males have some form of color-blindness, 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).
a. X and Y are binomial RVs. Identify n and p for each.
b. Can variables X and Y be well-approximated by normal random variables?
c. What is the number of possible outcomes consisting of 5 males being colorblind?
d. How many women on average do you expect to be colorblind?