Answer:
Explanation:
To find the probability that the whole shipment will be accepted, we can use the binomial probability formula:
**P(X = k) = (n choose k) * (p^k) * (q^(n-k))**
Where:
- n is the number of trials (number of tablets tested), which is 43 in this case.
- k is the number of successful trials (defects allowed), which is 0 or 1 in this case.
- p is the probability of a successful trial (probability of a tablet being defective), which is 4% or 0.04.
- q is the probability of an unsuccessful trial (probability of a tablet meeting the required specification), which is 1 - p = 0.96.
Now, we'll calculate the probability of accepting the whole shipment, which means having either 0 or 1 defective tablet out of 43 tested.
For k = 0:
**P(X = 0) = (43 choose 0) * (0.04^0) * (0.96^43)**
**P(X = 0) = 1 * 1 * (0.96^43)**
For k = 1:
**P(X = 1) = (43 choose 1) * (0.04^1) * (0.96^42)**
Now, we calculate both probabilities and sum them to find the total probability of accepting the shipment:
**P(acceptance) = P(X = 0) + P(X = 1)**
Calculate both probabilities and sum them:
**P(X = 0) = (0.96^43) ≈ 0.5834**
**P(X = 1) = (43 choose 1) * (0.04) * (0.96^42) ≈ 0.3852**
Now, find the total probability of acceptance:
**P(acceptance) ≈ 0.5834 + 0.3852 ≈ 0.9686**
So, the probability that this whole shipment will be accepted is approximately 0.9686 or 96.86%. This means that almost all such shipments will be accepted, as the probability of acceptance is quite high.