A shipment of electronic parts are sampled by testing items

A shipment of electronic parts are sampled by testing items sequentially until the first defective part is found. If 10 or more parts are tested until the first defective part is found, the shipment is accepted as meeting specifications.

a) Determine the probability that the shipment will be accepted if it contains 10% defective parts.

b) How many need to be sampled if it is desired that a shipment with 25% defective parts be rejected with probability of at least 0.75? That is, if n or more parts are tested in order for the first defective part to be found, the shipment is accepted as meeting specifications. Find the smallest n that rejects with a probability of at least 0.75, a shipment with 25% defective parts.

Solution

P =prob for defect = 10% = 0.1

Prob (accepted) = P(first parts not defective >=10)

=1-P(defects <10)

= 1- 0.1¹⁰

= 0.999999

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b) Here p =0.25

P(x>=n)

= 1-P(X<n)

1-0.25ⁿ>=0.75

Or 0.25ⁿ<=0.25

n should be greater than 1.