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Harrizon [31]
3 years ago
8

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.
Mathematics
1 answer:
Colt1911 [192]3 years ago
6 0

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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