Answer:
The probability that the whole shipment will be accepted is 0.5862.
Step-by-step explanation:
Let <em>X</em> = number of the aspirin tablets that doesn't meet the required specifications.
The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.03.
The sample of <em>n</em> = 47 tablets are tested from each batch.
The probability of any of the tablets being defective is independent of the others.
The probability mass function of <em>X</em> is,
Compute the probability that the whole shipment of 3000 tablets will be accepted as follows:
P (X ≤ 1) = P (X = 0) + P (X = 1)
Thus, the probability that the whole shipment will be accepted is 0.5862.
The sample of 47 tablets is significantly small when drawn from a population of 3000 tablets. So it is difficult to make conclusion about all such shipments of aspirin tablets.