Find the probability that follows Binomial distribution.

The following four problems refer to the following information:

Colourblindness is any abnormality of the colour vision system that causes a person to see colours differently than most people or to have difficulty distinguishing among certain colors.

Colourblindness is gender-based with the majority of sufferers being males.

Roughly 8 percent of white males have some form of colour blindness, while the incidence among white females is only 1 percent.

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 colourblind.

Let Y be the number of females (out of the 40) who are colourblind.

Let Z be the total number of colourblind 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 colourblind? (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 normal random variable.

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

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