Show me the complete systematic solution for this one. Thank you.

1. The diameter of holes for cable harness is known to have a standard deviation of 0.01 inches. A random sample of size 10 yields an average diameter of 1.5045 inches. Use a 0.01 level of significance.

a. Test the hypothesis that the true mean hole diameter equals 1.50.

b. What is the P-value for this test?

c. What size sample would be necessary to detect a true mean hole diameter of 1.505 inches with probability of at least 90%

d. What is the probability of committing a type 2 error if the true diameter is 1.505 inches?

e. Find a 99% confidence interval on the mean hole diameter.