A pharmaceutical company receives large shipments of aspirin tablets. The accept

Question

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 22 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4.0% rate of defects, what is the probability that this whole shipment will be accepted? The probability that this whole shipment will be accepted is (Round to three decimal places as needed.)

Explanation / Answer

sol:

n=10

p=probability of success=5%=0.05

q=failure =1-p=1-0.05=0.95

P(Atmost2)=P(X=0)+P(X=1)+P(X=2)

=10C0(0.05)0(1-0.05)10-0+10C1(0.05)1(1-0.05)10-1+10C2(0.05)2 (1-0.05)10-2

=0.5987+0.3151+0.0746

ANS:0.988

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