Suppose X,Y,and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that Xis a normal random variable having a mean of 15 cm and a standard deviation of 1 cm, and Y is independent of X and normally distributed with a mean of 25 cm and a standard deviation of 2 cm. Determine the following.
(a) the expected value of the perimeter
(b) the standard deviation of the perimeter
(c) the probability that the perimeter is between 76 cm and 82 cm
(d) the perimeter that is exceeded by 99% of the sheet metal parts