Final answer:
To calculate the probability of accepting the whole shipment, we need to determine the probability of finding one or no defective tablets in a random sample of 44 tablets. The shipment has a 3% rate of defects, and we can use the binomial probability formula to calculate the probabilities. Finally, we add the probabilities of getting 0 and 1 defective tablets to find the total probability of accepting the shipment.
Step-by-step explanation:
To calculate the probability that the whole shipment will be accepted, we need to determine the probability of finding one or no defective tablets in a random sample of 44 tablets from the shipment.
The shipment has a 3% rate of defects, which means that out of 5000 tablets, 3% or 150 tablets are defective. To find the probability, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k defective tablets
- C(n, k) is the number of ways to choose k defective tablets from n total tablets
- p is the probability of a single tablet being defective (3% or 0.03)
- n is the sample size (44)
In this case, we want to find the probability of getting 0 defective tablets (k = 0) or 1 defective tablet (k = 1). So:
P(X = 0) = C(44, 0) * 0.03^0 * (1-0.03)^(44-0)
P(X = 1) = C(44, 1) * 0.03^1 * (1-0.03)^(44-1)
Finally, we can calculate the total probability of accepting the whole shipment by adding the probabilities of getting 0 and 1 defective tablets:
P(accepting the shipment) = P(X = 0) + P(X = 1)