Question

A battery manufacturer makes batteries that have a failure rate of .015. That is, 15 out of each 1,000 batteries are defective. What is the probability

that a batch of 10,000 batteries will contain at least 175 defective batteries?

Answer 1

p(success) = 0.015
p(failure) = 1 - 0.015 = 0.985
let x be the random variable that a battery is defective, then
p(x >= 175) = 1 - P(x <= 175)
= 1 - P[z <= (175 - np)/(sqrt(npq))]
= 1 - P[z <= (175 - 10000 * 0.015)/(sqrt(10000 * 0.015 * 0.985))]
= 1 - P[z <= (175 - 150)/(sqrt(147.75))]
= 1 - P[z <= (25/12.16)]
= 1 - P(z <= 2.057)
= 1 - 0.9801
= 0.0199