The quality control unit in a medical device company inspect

The quality control unit in a medical device company inspects 20 pacemakers each hour. Let X represent the number of pacemakers in the sample of 20 that require rework. Pacemakers are assumed to be independent with respect to rework.

If the percentage of pacemakers that require rework remains constant at 1%, what is the probability that hour 5 is the first sample at which X exceeds 1?

If the rework percentage increases to 2%, what is the probability that hour 5 is the first sample at which X exceeds 1?

Solution

X is binomial with p = 0.01 and n =20

P(X<=1 in the first 4 hours) = 0.9831⁴=0.9341

Let p =0.02

P(X<=1 in the first 4 hours) = 0.6676⁴ = 0.1986