Question

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 doesnt meet the required specifications. if one shipment of 4000 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? the probability that this whole shipment will be accepted is 0.8382. (round to four decimal places as needed.) the company will accept % of the shipments and will reject % of the shipments, so (round to two decimal places as needed.)

Explanation:

Step1: Identify acceptance - probability

The probability that the shipment is accepted is given as \(P(\text{accepted}) = 0.8382\).

Step2: Calculate acceptance percentage

To convert the probability to a percentage, we use the formula \(\text{Percentage}=\text{Probability}\times100\). So, the acceptance percentage is \(0.8382\times100 = 83.82\%\).

Step3: Calculate rejection percentage

Since the total percentage is \(100\%\), the rejection percentage is \(100 - 83.82=16.18\%\).

Answer:

The company will accept \(83.82\%\) of the shipments and will reject \(16.18\%\) of the shipments. So almost all such shipments will not be accepted (because the rejection - rate is non - negligible).