Suppose the research department of a steel manufacturer believes that one of the company’s rolling machines is producing sheets of steel of varying thickness. The thickness is a uniform random variable with values between 150 and 200 millimeters. Any sheets less than 160 millimeters must be scrapped because they are unacceptable to buyers.

a. Calculate and interpret the mean and standard deviation of x, the thickness of the sheets produced by this machine.

b. Graph the probability distribution of x, and show the mean on the horizontal axis. Also show 1- and 2-standard-deviation intervals around the mean.

c. Calculate the fraction of steel sheets produced by this machine that have to be scrapped.