As the situation of Exercise 2.73 might suggest, statistical procedures are often used for control of quality (i.e., industrial quality control). At times, the weight of a product is an important variable to control. Specifications are given for the weight, of a certain packaged product and a package is rejected if it is either too light or too heavy. Historical data suggest that 0.95 is the probability that the product meets weight specifications whereas 0.002 is the probability that the product is too light. For each single packaged product the manufacturer invests $20.00 in production and the purchase price by the consumer is $25.00.

(a) What is the probability that a package chosen randomly from the production line it too heavy?

(b) For each 10,000 packages sold, what profit is received by the manufacturer if all packages meet weight specification?

(c) Assuming that all "defective" packages are rejected and rendered worthless, how much is the profit reduced on 10,000 packages due to failure to meet weight specification?