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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 = ?
Answer:
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
