A drug test is accurate 96% of the time. If the test is given to 2200 people, who have not taken drugs, what is the probability that at least 92 will test positive?

Question

A drug test is accurate 96% of the time. If the test is given to 2200 people, who have not taken drugs, what is the probability that at least 92 will test positive?

Answer 1

Well probability that one will test positive = 1 - 0.96 = 0.04

We need p (X>=92) with a binomial distribution, p = 0.04, n = 2200

On a TI-84

binomcdf

trials = 2200

p = 0.04

x value = 91

0.6536

This is p (X<=91) so we take this away from 1, giving p (X>=92) = 1 - 0.6536 = 0.3464