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 100 and 200 millimeters. Any sheets less than 120 millimeters must be scrapped because they are unacceptable to buyers.
1) Calculate the mean and standard deviation of thickness.
2) Graph the pdf of the random variable and show the mean on the horizontal axis. Also show 1 and 2 standard deviation intervals around mean.
3) Calculate the fraction of steel sheets produced by this machine that have to be scrapped.