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 = ?

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

You question is not complete. Below is the complete question.

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. 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.

Answer:

Mean = 0.4

Standard deviation = 0.02

Step-by-step explanation:

Solution:

Data Given;

Colorblindness in white males = 8%

Colorblindness in white female 1%

Number of males sample = 20

Number of female sample = 40

standard deviation female sample (sample Y) ?

Mean of female sample (Y) ?

To calculate the mean of the variable Y (female), we use the formula;

mean = n*p

= 40 * 1/100

= 40 * 0.01

= 0.4

Calculating the standard deviation of variable Y (female), we use the formula;

Standard deviation = √p (1 - p) / n

= √0.01 (1 - 0.01) / 40

= √0.01 (0.99) / 40

= √0.0099/40

= √0.0002475

= 0.0157 = 0.02 approximately