Let the random variable X denote a measurement from a manufactured product. Suppose the target value for the measurement is m. For example, X could denote a dimensional length, and the target might be 10 millimeters. The quality loss of the process producing the product is defined to be the expected value of

, where k is a constant that relates a deviation from target to a loss measured in dollars.

(a) Suppose X is a continuous random variable with and . What is the quality loss of the process?

(b) Suppose X is a continuous random variable with and . What is the quality loss of the process?