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bout 10% of the population has a particular genetic mutation. 100 people are randomly selected.Find the standard deviation for the number of people with the genetic mutation in such groups of 100.

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Let x be a random variable denoting the number of people having genetic mutation out of 100 people.

x follows Binomial Distribution with parameters:

n = 100

p = 10% = 0.10

So, The standard deviation of x is:


\text{standard deviation=}\sqrt[]{np(1-p)}

Substitute the values:


=\sqrt[]{100*0.10*(1-0.10)}

Simplify:


\begin{gathered} =\sqrt[]{100*0.10*0.90} \\ =\sqrt[]{9} \\ =3 \end{gathered}

Answer: the standard deviation is 3

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