Question

a pharmaceutical company receives large shipments of aspirin tablets. the acceptance sampling plan is to randomly select and test 57 tablets, then accept the whole batch if there is only one or none that doesnt meet the required specifications. if one shipment of 3000 aspirin tablets actually has a 3% 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 0.4868.
(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: Calculate the proportion of accepted shipments

The probability that a shipment is accepted is \(P(\text{accepted}) = 0.4868\). To convert this to a percentage, we use the formula \( \text{Percentage} = P\times100\). So, \(0.4868\times100 = 48.68\%\). Rounding to two decimal places, it remains \(48.68\%\).

Step2: Calculate the proportion of rejected shipments

Since the total proportion of shipments is \(1\) (or \(100\%\)), the probability of rejection \(P(\text{rejected})\) is \(1 - P(\text{accepted})\). So, \(1- 0.4868=0.5132\). Converting to a percentage: \(0.5132\times 100 = 51.32\%\). Rounding to two decimal places, it remains \(51.32\%\).

Answer:

The company will accept \(48.68\%\) of the shipments and will reject \(51.32\%\) of the shipments.