An inspector working for a manufacturing company has a 99 ch

An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defective. The company has evidence that its line produces 0.8% of nonconforming items. Round your answers to five decimal places (e.g. 98.76543).

a) What is the probability that an item selected for inspection is classified as defective?

b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?

Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2 and 1% of the sample shipped in small and large packages, respectively, break during transit. If 56% of the samples are shipped in large packages and 44% are shipped in small packages, what proportion of samples break during shipment? Round your answer to four decimal places (e.g. 98.7654).

Solution

D = Item is defective
G = Item is not defective (Good)
SD = Item is classified as defective
SG = Item is classified as not defective (Good)

P(D) = 0.008
P(G) = 0.992
P(SD|D) = P(SD?D) / P(D) = 0.99
P(SG|D) = .01
P(SD|G) = 0.005
P(SG|G) = 0.995



(a) P(SD) = P(SD ? G) + P(SD ? D)
= P(SD|G) / P(G) + P(SD|D) / P(D)
=.005 * .992 + .99 * .008
=.01288 Ans.

b).
P[good & classified good] = .992 - .00496 = 0.98704
P[bad & classified as good] = .008 - .00792 = 0.00008
P[good|classified good] = 0.98704/(0.98704+0.00008) = 0.9999189 Ans.

c). Small packages : 44% of 2% = (.44)(.02) = .0088 = proportion that break
Large packages: 56% of 1% = (.56)(.01) = .0056 = proportion that break

= .0088 + .0056 = 0.0144 Ans.