A Contract Calls for the Mean Diameter of a Cylinder

Multiple Choice

A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality check, each day a random sample of n = 36 cylinders is selected and the diameters are measured. Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025, what would the probability of a Type II error be?

A) Approximately 0.1267
B) About 0.6789
C) 0.975
D) Can't be determined without knowing the "true" population mean.