A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 36 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 2% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Accepted Solution
A:
Answer:The probability that this whole shipment will be accepted is 0.8382. Almost all such shipments be accepted as the probability of accepting is higher. Step-by-step explanation:Consider the provided information.The probability for accepting the whole batch if there is only one or none that doesn't meet the required specifications.Aspirin tablets actually has a 2% rate of defects. Thus, the rate of aspirin tablets are not defected 98%.Which can be written as:P(x=0 or x=1)P(no defects out of 36)=[tex]^{36}c_0 \times (0.02)^0 \times (0.98)^{36}[/tex]P(no defects out of 36)=[tex]0.483213128206[/tex]P(one defects out of 36)=[tex]^{36}c_1 \times (0.02)^1 \times (0.98)^{35}[/tex]P(one defects out of 36)=[tex]36 \times 0.02 \times (0.49307)[/tex]P(one defects out of 36)=[tex]0.3550104[/tex]The probability that the whole shipment will accepted is the sum of the individual probabilities which is:0.4832+0.3550=0.8382Hence, the probability that this whole shipment will be accepted is 0.8382. Almost all such shipments be accepted as the probability of accepting is higher.