During the manufacturing of commercial windows, hot steel ingots are passed though a rolling process and flattened to a prescribed thickness. When the manufacturing process is working properly the ingots should have a mean thickness of 0.75 inches. A random sample of 40 ingots is taken and the mean was found to be 0.725 inches with a standard deviation of 0.092.
a. Find a 95% confidence interval for the population mean thickness.
b. Find the error bound.
c. Interpret the confidence interval in the words of the problem.
d. Is there evidence that the machine is not functioning properly? Justify!