3.Phnom Penh Plumbing maintains a stock of 100 liter hot water heaters that it sells. The owner likes the idea of having a large supply on hand to meet customer demand, but he also recognizes that it is expensive to do so. He examines hot water heater sales over the past 50 weeks and notes the following:

HOT WATER HEATER NUMBER OF WEEKS SALES PER WEEK THIS NUMBER WAS SOLD 1 00 -1 0 Up 12 10 Total 50 HOT WATER HEATER RANDOM SALES PROBABILITY NUMBER INTERVAL .12 01-12 .10 13-22 .18 23-40 .24 41-64 .16 65-80 .14 81-94 06 95-00 Total 1.00 RANDOM SIMULATED RANDOM SIMULATED WEEK NUMBER SALES WEEK NUMBER SALES 10 N 24 18 03 13 66 32 14 97 10 23 15 03 59 16 96 95 17 46 34 18 74 51 20 (a) If Phnom Penh Plumbing maintains a constant supply of 8 hot water heaters in any given week, how many times will he be out of stock during a 20-week simulation? (b) What is the average number of sales per week (including stockouts) over the 20-week period? (c) Using the expected value technique, what is the expected number of sales per week? How does this compare with the answer in part b