Question

About 6% 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

Answer:

The standard deviation for the number of people with the genetic mutation in such groups of 100=$2.375$

Step-by-step explanation:-

We are given that

Total number of selected people, n=100

p=6%=0.06

We have to find the standard deviation for the number of people with the genetic mutation in such groups of 100.

Let X denote the number of people  with the genetic mutation in such groups of 100.

$\implies X\sim Bin(n=100,p=0.06)$

We know that

Standard deviation

=$\sqrt{np(1-p)}$

Using the formula

Standard deviation

=$\sqrt{100\times 0.06(1-0.06)}$

=$\sqrt{6(0.94)}$

=$2.375$

Hence, the standard deviation for the number of people with the genetic mutation in such groups of 100=$2.375$