Nike ONE Black is one of the golf balls Nike, Inc., produces. It must meet the specifications of the United States Golf Association (USGA). The USGA mandates that the diameter of the ball shall not be less than 1.682 inches (42.67 mm). To verify that this specification is met, sample golf balls are taken from the production line and measured. These data are found in the file titled Diameter.

a. Calculate the mean and standard deviation of this sample.

b. Examine the specification for the diameter of the golf ball again. Does it seem that the data could possibly be bell shaped? Explain.

c. Determine the proportion of diameters in the following intervals:

x̅ ± 2s, x̅ ± 3s, x̅ ± 4s.

Compare these with the percentages specified by Tchebysheff’s theorem.