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

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

=
`√(np(1-p))`

Using the formula

Standard deviation

=
`√(100* 0.06(1-0.06))`

=
`√(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`