Question

About 5% of the population has a particular genetic mutation. 1000 people are randomly selected.

Find the standard deviation for the number of people with the genetic mutation in such groups of 1000.

Answer 1

`\simeq 6.89202`

Explanation:

Let, X = Number of people with the genetic mutation in such groups of 1000

Here, we get a random variable X with binomial distribution with parameters

n = 1000 and p = 5 % = 0.05

So,

X
`\sim` bin ( 1000 , 0.05)

so V(X) or Variance(X) =
`n * p * (1 -p)`

= 47.5

So, SD(X) = Standard Deviation(X) =
`\sqrt (47.5)`

`\simeq 6.89202`