Question

A certain large manufacturing facility produces 20,000 parts each week. The manager of the facility estimates that about 1% of the parts they make are defective. What is the variance for the number of defective parts made each week

Answer 1

198 is the variance for the number of defective parts made each week.

Explanation:

We are given the following in the question:

Number of parts produced each week = 20,000

Percentage of defective parts = 1%

We have to calculate the variance for the number of defective parts made each week.

We treat defective part as a success.

P(Defective part) = 1% = 0.01

`p = 0.01`

Then the number defective parts follows a binomial distribution .

Formula for variance =

`\sigma^2 = np(1-p) = 20000(0.01)(1-0.01) = 198`

Thus, 198 is the variance for the number of defective parts made each week.