The uniform length of nails is very important to a carpenter—the length of the nails being used are matched to the materials being fastened together, thereby making a small standard deviation an important property of the nails. A sample of 35 randomly selected 2-inch nails is taken from a large quantity of Nails, Inc.’s, recent production run. The resulting length measurements have a mean length of 2.025 inches and a standard deviation of 0.048 inch.

a. Determine whether an assumption of normality is reasonable. Explain.

b. Does the sample evidence show sufficient evidence to reject the idea that the nails have a mean length of 2 inches? Use   0.05.

c. Is there sufficient evidence, at the 0.05 level, to show that the length of nails from this production run have a standard deviation greater than the advertised 0.040 inch?

d. Write a short report outlining the findings and recommendations as to whether or not the carpenter should use these nails for an application that requires 2-inch nails.