A new process has been designed to make ceramic tiles. The goal is to have no more than 5% of the tiles be nonconforming due to surface defects. A random sample of 1000 tiles is inspected. Let p̂ be...

A new process has been designed to make ceramic tiles. The goal is to have no more than 5% of the tiles be nonconforming due to surface defects. A random sample of 1000 tiles is inspected. Let p̂ be the proportion of nonconforming tiles in the sample.

a) If the sample proportion of nonconforming tiles were 0.075, would it be pausible that the goal had been reached? Explain.

b) If 5% of the tiles produced are nonconforming, what is P (p̂ ≥ 0.075)?

c) Based on the answer to part a, if 5% of the tiles are nonconforming, is a proportion of 0.075 nonconforming tiles in a sample of 1000 unusually large?