Question

section 6.2 homework
score: 7.32/14 answered: 9/14
question 11
about 4% of the population has a particular genetic mutation. 800 people are randomly selected.
find the standard deviation for the number of people with the genetic mutation in such groups of 800.
round answer to two decimal places.

Explanation:

Step1: Identify the binomial - distribution parameters

This is a binomial - distribution problem where \(n = 800\) (sample size) and \(p=0.04\) (probability of success, i.e., having the genetic mutation). The formula for the standard deviation of a binomial distribution is \(\sigma=\sqrt{np(1 - p)}\).

Step2: Substitute the values into the formula

Substitute \(n = 800\), \(p = 0.04\), and \(1-p=0.96\) into the formula \(\sigma=\sqrt{np(1 - p)}\). So, \(\sigma=\sqrt{800\times0.04\times0.96}\).
First, calculate \(800\times0.04\times0.96=800\times0.0384 = 30.72\). Then, \(\sigma=\sqrt{30.72}\approx5.54\).

Answer:

5.54