Parker Seal, Inc. makes O-rings for newly planned commercial space shuttles. The rings are designed to seal connections and joint fillings in the fuel system to prevent leaks. One type of ring should be 5 centimeters in diameter in order to fit properly. A sample of 49 of these types of O-rings is selected and the diameters are measured the sample results are as follows:

Sample Size = 49

Sample Mean = 5.05 centimeters.

Sample Standard Deviation = .14 centimeters.

a. Construct a 99% confidence interval for the average diameter of this type of O-Ring.

b. Interpret this interval.

c. How large a sample size will need to be selected if we wish to have a 99% confidence interval for the average diameter of this type of O-Ring with a margin for error of .02 centimeters?