Final answer:
The probability that the whole shipment of 7000 aspirin tablets will be accepted is 1.
Step-by-step explanation:
The acceptance sampling plan for the pharmaceutical company states that if one or none of the 44 tablets tested in a shipment of 7000 aspirin tablets does not meet the required specifications, the whole batch will be accepted. In this case, the shipment has a 2% rate of defects. We want to find the probability that the whole shipment will be accepted.
To find the probability, we need to calculate the probability that none or only one tablet out of the sample of 44 is defective. We can use the binomial probability formula for this: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the sample size, k is the number of successes, C(n, k) is the combination of n items taken k at a time, and p is the probability of success.
In this case, n = 44, k can be 0 or 1, p = 0.02 (2% defect rate).
Plugging in the values:
P(X=0) = C(44, 0) * (0.02)^0 * (1-0.02)^(44-0) = 0.887
P(X=1) = C(44, 1) * (0.02)^1 * (1-0.02)^(44-1) = 0.113
The probability that none or only one tablet in the shipment of 7000 aspirin tablets is defective and the whole batch is accepted is the sum of these probabilities: P(X <= 1) = P(X=0) + P(X=1) = 0.887 + 0.113 = 1
Therefore, the probability that this whole shipment will be accepted is 1.