Chapter 5.2, Problem 48E

Equipment Breakdowns. The factory manager in Exercise 5.43 estimates that each breakdown costs the company $500 in repairs and loss of production. If W is the number of breakdowns in a day, then $500W is the cost of breakdowns for that day.

1. a. Refer to the probability distribution shown in Exercise 5.43 and determine the probability distribution of the random variable 500W.
2. b. Determine the mean daily breakdown cost, μ_500W, by using your answer from part (a).
3. c. What is the relationship between μ_500W and μ_W? (Note: From Exercise 5.43, μ_W = 0.25.)
4. d. Find σ_500W by using your answer from part (a).
5. e. What is the apparent relationship between σ_500W and σ_W? (Note: From Exercise 5.43, σ_W = 0.536.)
6. f. The results in parts (c) and (e) hold in general: If W is any random variable and c is a constant,

   μ_cW = cμ_W and σ_cW = |c|σ_W.

   Interpret these two equations in words.