An electric component for a medical xray unit is produced in lotsof size n=25. A

Question

An electric component for a medical xray unit is produced in lotsof size n=25. An acceptance testing procedure is used by thepurchaser to protect against lots that contain too manynonconforming components. The procedure consists of selecting 5components at random from the lot (without replacement) and testingthem. If none of the components is nonconforming, the lot isaccepted.
a)If the lot contains 2 nonconforming components, what is theprobability of lot acceptance?
b)Calculate the desired probability in (a) using binomialapproximation. Is this approximation satisfactory? why or whynot?
c)suppose the lot size was N=150 would the binomial approximationbe satisfactory in this case?
d)Suppose the purchase will reject the lot with the decision's ruleof finding one or more nonconforming components in a sample size ofn and wants the lot to be rejected with the probability at least.95 if the lot contains 5 or more nonconforming components. Howlarge should the sample size n be?

Explanation / Answer

a) P = 23/25 * 22/24 * 21/23 * 20/22 * 19/21 = 19/30 = 0.633 b) P = binompdf(5,23/25,5) = 0.659. This approximation is notsatisfactory, because the parts are chosen without replacement, andthe lot is 25 and 25 is not that many times bigger than the 5selected. c) if the lot size was 150, the 5 would be a small enough fractionthat we could use the approximation d) P = 20/25 * 19/24 * .... * (21-n)/(26-n) < 1 - .95 =.05 20!/(20-n)! * (25-n)!/(25)! < .05 n = 11

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