The time between emergency calls at the 9-1-1 emergency call service of a Pennsylvania township has the following probability distribution. The 91-1 service sends emergency responders 24 hours per day, 7 days per week:

1. From the probability distribution, compute the expected value of the time between calls.

2. Using a random number table, simulate the emergency calls for 2 days. (Use a €œrunning€ or cumulative, hourly clock), and compute the average time between calls.

3. Compare the values obtained in (a) and (b). Provide an explanation for the different results.

Data from example d.1

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Time Betvween Emergency Calls (in hours) 2 3 4 5 0.20 0.04 0.20 Probability 0.06 0.10 0.15 0.15 0.10 TABLE D.7: Demand and Lead Time Frequency Distribution for Microwave Ovens DEMAND FOR FREQUENCY OF LEAD TIME FOR FREQUENCY OF MICROWAVE OVENS OCCURRENCE (IN DAYS) MICROWAVE OVENS OCCURRENCE (IN DAYS) 20 20 40 2 50 70 30 3 60 4 20 10 Total = 200 Total = 100