What is the mean and standard deviation of the random variable Y (the number of females out of 40 who are color blind)? Answers may be rounded.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

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 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.

What is the mean and standard deviation of the random variable Y (the number of females out of 40 who are color blind)? Answers may be rounded.

Given Information:

Female colorblindness proportion = 1%

Male colorblindness proportion = 8%

Female sample size = 40

Male sample size = 20

Required Information:

Mean = μ = ?

Standard deviation = σ = ?

Mean = μ = 0.40

Standard deviation = σ = 0.015

Step-by-step explanation:

Let us check if the condition np ≥ 10 is satisfied or not

np

40*0.01

0.4 < 10

Since the condition np ≥ 10 is not satisfied the binomial random variable cannot be well approximated by a normal random variable. A larger sample size would be required to satisfy the condition np ≥ 10.

The mean is

μ = np

μ = 40*0.01 = 0.40

The standard deviation is

σ = √p(1 - p)/n

σ = √0.01(1 - 0.01)/40

σ = 0.015