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)}](https://img.qammunity.org/2023/formulas/mathematics/college/ze9ysvvd6yuzg50ypqavx6otr0lh3t9t49.png)
Substitute the values:
![=\sqrt[]{100*0.10*(1-0.10)}](https://img.qammunity.org/2023/formulas/mathematics/college/lqzzrmlcu36gi87tknhp1s9xrgvfu3m5e4.png)
Simplify:
![\begin{gathered} =\sqrt[]{100*0.10*0.90} \\ =\sqrt[]{9} \\ =3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/72lng4gl1ory1q0rnfudqjrj6weodey5h3.png)
Answer: the standard deviation is 3