A manufacturer produces 1000 computer chips for a mission-critical application. Each chip costs $100 to manufacture and sells for $2000, but has a 1% chance of being defective.
a) Compute the mean and standard deviation of the number of defective chips.
b) Assume that 99.9% of defective chips are discovered (and destroyed) before they are sold, while the other 0.1% are sold with defects. The manufacturer suffers an estimated loss of $20,000,000 for each defec- tive chip sold (due to lawsuits, penalties, and bad public relations). What is the manufacturer's expected profit?
c) The manufacturer develops a new quality control technology which enables detection of 100% of de- fective chips. How much would the implementation of this technology increase the manufacturer's expected profit?