Find the probability that follows Binomial distribution.

The following four questions refer to the following information:

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.xom).

Colorblindness 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 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).

1.  Which of the following is true about the random variables X, Y, and Z?

a.X is binomial with n = 20 and p = .08.

b.Y is binomial with n = 40 and p = .01.

c.Z is not binomial.

d.All of the above are true.

e.Only (a) and (b) are true.

2. What is the probability that exactly 2 of the 20 males are colorblind? (Note: Some answers are rounded.)

a. .08

b. .2711

c. .0143

d. .5422

e. .0159

3.  What is the mean of Z, the expected total number of individuals (males and females) who are colorblind? (Hint: Express Z in terms of X and Y and then apply rules for means.)

a. .4

b.1.6

c. 2

d. 2.7

e. The mean of Z cannot be determined.

4. Which of the following is true regarding the random variables X and Y?

a. Both X and Y can be well-approximated by normal random variables.

b. Only X can be well-approximated by a normal random variable.

c. Only Y can be well-approximated by a normal random variable.

d. Neither X nor Y can be well-approximated by a normal random variable.