Question

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.

Answer 1

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:

$=\sqrt[]{100\times0.10\times(1-0.10)}$

Simplify:

$\begin{gathered} =\sqrt[]{100\times0.10\times0.90} \\ =\sqrt[]{9} \\ =3 \end{gathered}$

Answer: the standard deviation is 3