In manufacturing a certain item, historically it has been found that 95% of the

Question

In manufacturing a certain item, historically it has been found that 95% of the items are good, 4% are “seconds”, and 1% are defective.   Each hour, an on-line inspector observes 20 items selected at random and classifies them according to the three categories.   a. Find the probability that all 20 of the items are good. b. Find the probability that there are 18 good items, 1 “second”, and 1 defective item. c. Find the expected number of defective items. d. Find the correlation between the number of “seconds” and the number of defective items.

Explanation / Answer

a) probability that all 20 of the items are good =(0.95)20 =0.3585

b) probability that there are 18 good items, 1 “second”, and 1 defective item=(20!/(18!*1!*1!))*(0.95)18(0.04)1*(0.01)1

=0.0604

c)expected number of defects =np=20*0.01=0.2

d)correlation between the number of “seconds” and the number of defective items=0; as both these events are independent

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