Question

About 7% of the population has a particular genetic mutation. 200 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 200.

Answer 1

To find the standard deviation for the number of people with the genetic mutation in groups of 200, use the formula for the standard deviation of a binomial distribution.

Step-by-step explanation:

To find the standard deviation for the number of people with the genetic mutation in groups of 200, we need to use the formula for the standard deviation of a binomial distribution. In this case, the probability of success (having the genetic mutation) is 0.07, and the sample size is 200.

The formula for the standard deviation of a binomial distribution is:

σ = sqrt(np(1-p))

where σ is the standard deviation, n is the sample size, and p is the probability of success.

Plugging in the values, we get:

σ = sqrt(200 * 0.07 * (1 - 0.07))

σ ≈ sqrt(200 * 0.07 * 0.93)

σ ≈ sqrt(12.6)

σ ≈ 3.55

Therefore, the standard deviation for the number of people with the genetic mutation in groups of 200 is approximately 3.55.