\fSteel is to be cut and the resulting parts are to be within +0.005 inch of the length specified by the purchaser. The measurement reported from a sample of 30 steel parts (and available below) is the difference, in inches, between the actual length of the steel part and the specified length of the steel part. For example, the first observation, 0.0008, represents a steel part that is 0.0008 inch shorter than the specified length. Complete parts (a) through (d) below. Click here to view the differences data. Click here to view a percentage histogram of the differences data. a. Construct a 95% confidence interval estimate of the population mean difference between the actual length of the steel part and the specified length of the steel part. =p= (Round to five decimal places as needed.) b. What assumption must you make about the population distribution in order to construct the confidence interval in (a)? () A. The population distribution is not nermally distributed. () B. The population distribution is uniformly distributed. ) C. The population standard deviation is known. () D. The population distribution is unimodal and not extremely skewed. c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain. The assumption is v forn= since v d. Is the steel mill doing a good job meeting the requirements set by the purchaser? Explain. Does the percentage histogram support this conclusion? Since the confidence interval v within 0.005 inch of 0, the steel mill and | are greater than 0.005 inch from 0. v doing a good job. The percentage histogram v this conclusion because of the differences are near 0 Percentage Histogram 40+ 30- % Total 20- 10- -0.006 -0.003 0.000 0.003 0.006 Difference (inches)