Example Problem Solution

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The following example problem demonstrates a manual simulation using discrete probability distributions.

Problem Statement

Members of the Willow Creek Emergency Rescue Squad know from past experience that they will receive between zero and six emergency calls each night, according to the following discrete probability distribution:

Calls	Probability
	.05
1	.12
2	.15
3	.25
4	.22
5	.15
6	.06
	1.00

The rescue squad classifies each emergency call into one of three categories: minor, regular, or major emergency. The probability that a particular call will be each type of emergency is as follows :

Emergency Type	Probability
Minor	.30
Regular	.56
Major	.14
	1.00

The type of emergency call determines the size of the crew sent in response. A minor emergency requires a two-person crew, a regular call requires a three-person crew, and a major emergency requires a five-person crew.

Simulate the emergency calls received by the rescue squad for 10 nights, compute the average number of each type of emergency call each night, and determine the maximum number of crew members that might be needed on any given night.

Solution

Step  1.

Develop Random Number Ranges for the Probability Distributions

Calls	Probability	Cumulative Probability	Random Number Range, r 1
	.05	.05	15
1	.12	.17	617
2	.15	.32	1832
3	.25	.57	3357
4	.22	.79	5879
5	.15	.94	8094
6	.06	1.00	9599,00
	1.00

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Emergency Type	Probability	Cumulative Probability	Random Number Range, r 2
Minor	.30	.30	130
Regular	.56	.86	3186
Major	.14	1.00	8799, 00
	1.00

Step  2.

Set Up a Tabular Simulation

Use the second column of random numbers in Table 14.3:

Night	r 1	Number of Calls	r 2	Emergency Type	Crew Size	Total per Night
1	65	4	71	Regular	3
			18	Minor	2
			12	Minor	2
			17	Minor	2	9
2	48	3	89	Major	5
			18	Minor	2
			83	Regular	3	10
3	08	1	90	Major	5	5
4	05
5	89	5	18	Minor	2
			08	Minor	2
			26	Minor	2
			47	Regular	3
			94	Major	5	14
6	06	1	72	Regular	3	3
7	62	4	47	Regular	3
			68	Regular	3
			60	Regular	3
			88	Major	5	14
8	17	1	36	Regular	3	3
9	77	4	43	Regular	3
			28	Minor	2
			31	Regular	3
			06	Minor	2	10
10	68	4	39	Regular	3
			71	Regular	3
			22	Minor	2
			76	Regular	3	11

Step  3.

Compute Results

If all the calls came in at the same time, the maximum number of squad members required during any 1 night would be 14.