Suppose that a batch of 100 items contains 10 defective. The quality control man

Question

Suppose that a batch of 100 items contains 10 defective. The quality control manager sequentially inspects 8 times. However, being sloppy and lacking formal statistical training, his random selection of items is with replacement (i.e. after an item is inspected it is placed back in the batch with the others). Let Xibe 0 as the item inspected in the i-th draw is non-defective, 1 otherwise, I = 1, 2, …, 8.

(a) The distribution of X3 is (circle only one specific answer):

Bernoulli       Binomial     Poisson     Geometric      Negative Binomial     Hypergeometric   

(b) Find P{X5 = 1}.

(c) LET X = X1 + X2 + …+ X8. The distribution of X defined here is (circle only one specific answer):

Bernoulli        Binomial      Poisson      Geometric       Negative Binomial      Hypergeometric

(d) Let A denote the event that X5 = 0 and B denote the event that the sample contains 3 defective items in the 8 inspected. Find P(BA). (Hint: given A, express the event B in terms of the number of defective items found in the inspections other than the 5-th).

Explanation / Answer

a) Bernoulli

b) 0.10

c) Binomial

d) P(B/A) =P(AB)/P(A) = 0.079365

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