About 7% of the population has a particular genetic mutation. 800 people are randomly selected. Find the standard deviation for the number o

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About 7% of the population has a particular genetic mutation. 800 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 800.

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Verity 3 years 2021-08-27T18:53:07+00:00 1 Answers 0 views 0

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  1. Neala
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    2021-08-27T18:54:19+00:00
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    Answer:

    The standard deviation is of 7.22 people.

    Step-by-step explanation:

    For each person, there are only two possible outcomes. Either they have the mutation, or they do not. The probability of a person having the mutation is independent of any other person, which means that the binomial probability distribution is used to solve this question.

    Binomial probability distribution

    Probability of exactly x successes on n repeated trials, with p probability.

    The expected value of the binomial distribution is:

    E(X) = np

    The standard deviation of the binomial distribution is:

    \sqrt{V(X)} = \sqrt{np(1-p)}

    About 7% of the population has a particular genetic mutation.

    This means that p = 0.07

    800 people are randomly selected.

    This means that n = 800

    Find the standard deviation for the number of people with the genetic mutation in such groups of 800.

    \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.07*0.93} = 7.22

    The standard deviation is of 7.22 people.

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