The Four Brothers Lumber Company is considering buying a machine that planes lumber to the correct thickness. The machine is advertised to produce “6-inch lumber” having a thickness that is normally distributed, with a mean of 6 inches and a standard deviation of 0.1 inch.
a. If building standards in the industry require a 99% chance of a board being between 5.85 and 6.15 inches, should Four Brothers purchase this machine? Why or why not?
b. To what level would the company that manufactures the machine have to reduce the standard deviation for the machine to conform to industry standards?