Question

The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution:

Time Between Emergency Calls (hours)	Probability
1	0.05
2	0.10
3	0.30
4	0.30
5	0.20
6	0.05
	1.00

The squad is on duty 24 hours per day, 7 days per week.

a. Simulate the emergency calls for three days (note that this will require a “running,” or cumulative, hourly clock) using the random number table.

Answer 1

Since the random number list is not given, we have generated them in this problem.

Step-1: Generate the random number ranges using the cumulative probability distribution as shown below.

Time Between Calls (hours)	Probability	CumProb	Random number ranges
1	0.05	0.05	00 - 04
2	0.10	0.15	05 - 14
3	0.30	0.45	15 - 44
4	0.30	0.75	45 - 74
5	0.20	0.95	75 - 94
6	0.05	1.00	95 - 99

Step-2: based on the random number ranges and the random number list, assign the time passed between calls, count the number of calls up to the cumulative time being less than or equal to 72 hrs. (3 days).

Day	Call	Random Number	Time passed	Cumulative time passed
1	1	42	3	3
1	2	67	4	7
1	3	90	5	12
1	4	100	6	18
1	5	86	5	23
2	6	15	2	25
2	7	13	2	27
2	8	29	3	30
2	9	42	3	33
2	10	72	4	37
2	11	50	4	41
2	12	80	5	46
3	13	35	3	49
3	14	94	5	54
3	15	87	5	59
3	16	43	3	62
3	17	59	4	66
3	18	42	3	69
Day 4	-	56	4	73 (> 72)

Note that, the simulation shows that 18 calls will be received in 3 days span.