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?
A) 138
B) 200
C) 198
D) 14.1

Question

Quizplus · Accepted Answer

The variance for a binomial distribution is given by the formula $ \sigma^2 = np(1-p) $, where $ n $ is the number of trials (in this case, parts produced per week, which is 20,000) and $ p $ is the probability of success (in this case, the probability of a part being defective, which is 0.01). Plugging in these values, we get $ \sigma^2 = 20,000 \times 0.01 \times (1-0.01) = 200 \times 0.99 = 198 $.

A Certain Large Manufacturing Facility Produces 20,000 Parts Each Week