A drug test is accurate 96% of the time. If the test is given to 1500 people who have not taken drugs, what is the probability that at least 61 will test positive?

Question

A drug test is accurate 96% of the time. If the test is given to 1500 people who have not taken drugs, what is the probability that at least 61 will test positive?

Answer 1

(s = probability of success. f = probability of failure = 1 - s. n = number of trials)

This is a binomial distribution with s = .04 and f = .96 and n = 1500.

60 is too many to calculate exactly, on an individual basis, so use the normal approximations.

mu = s * n = .04 * 1500 = 60

sigma = s * f * n = 57.6

use those to calculate your z score. then use your z score to calculate the probability that X is at least 61.