A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. Referring to the problem statement, suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be? Show work