Question

Whenever a cannery receives a shipment of 10000 to 15000 cans, the following rule is used to decide whether to accept or reject the shipment. Select a random sample of 171 cans from the shipment. If the proportion of nonconforming cans is 0.056 or more, reject the entire shipment; otherwise accept the shipment. What is the probability of accepting a shipment that really contains 8.7%(π) nonconforming cans ?

a. 9.6.1%
b. 3.9%
c. none
d.92.5%
e.7.5%

Answer 1

To find the probability of accepting a shipment with a nonconforming cans proportion of 8.7%, we need to calculate the sampling distribution.

Step-by-step explanation:

To find the probability of accepting a shipment that really contains 8.7% nonconforming cans, we need to calculate the proportion of nonconforming cans in a sample of 171 cans. If the proportion is 0.056 or more, the shipment will be rejected.

Since the proportion of nonconforming cans is 8.7% (or 0.087), we can use the normal distribution to approximate the sampling distribution of the sample proportions.

Using the formula for the standard error of the proportion, we can calculate the z-score and find the area under the standard normal curve to determine the probability.