Question

About 6% of the population has a particular genetic mutation. 600 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 600.

Answer 1

Assume a binomial distribution. Then the mean of the distribution is $np$, where $n$ is the number of people taken in a sample and $p$ is the probability of the mutation occurring in any given person, and the standard deviation is $\sqrt{np(1-p)}$. Then in this case, the standard deviation is $\sqrt{600(0.06)(0.94)}\approx5.82$.