5. A manufacturing process produces bolts. The distribution of bolt sizes is normally distributed with a diameter mean of 0.5 in and a standard deviation of .12 inches. Once each day a random sample of 20 bolts is selected and the diameters are recorded. Show your normal curve and calculator entries. Round answers to four decimal places.

a. What is the shape of the distribution of the sample means? Why?

b. What is the mean of the sample mean of bolt diameters?

c. What is the standard deviation of the distribution of sample means?

d. What is the probability of finding a sample with a mean less than 0.494 inches?

e. What mean bolt size would be in the top 10% of mean bolt sizes.

f. If you were to find a sample of 20 bolts with a mean diameter of .46 inches, would you have concerns about the manufacturing process?