Cooper Manufacturing, Inc., of Dallas, Texas, has a contract with the U.S. Air Force to produce a part for a new fighter plane being manufactured. The part is a bolt that has specifications requiring that the length be normally distributed with a mean of 3.05 inches and a standard deviation of 0.015 inch. As part of the company’s quality control efforts, each day Cooper’s engineers select a random sample of 100 bolts produced that day and carefully measure the bolts to determine whether the production is within specifications. The following data were collected yesterday:

Length (inches) Frequency Under 3.030 5 3.030 and under 3.035 16 3.035 and under 3.040 7 3.040 and under 3.050 20 3.050 and under 3.060 36 3.060 and under 3.065 8 3.065 and over 8 Based on these sample data, what should Cooper’s engineers conclude about the production output if they test using an a  0.01? Discuss.