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17 March, 14:56

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.

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  1. 17 March, 15:23
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    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
  2. 17 March, 16:32
    0
    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
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