Question

One of the large photocopiers used by a printing company has a number of special functions unique to that particular model. This photocopier generally performs well but, because of the complexity of its design and the frequency of usage, it occasionally breaks down. The department has kept records of the number of breakdowns per month over the last fifty months. The data is summarized in the table below:
  

Number of Breakdowns	Probability
0	0.12
1	0.32
2	0.24
3	0.20
4	0.08
5	0.04

  
The cost of a repair depends mainly on the time taken, the level of expertise required and the cost of any spare parts. There are four levels of repair. The cost per repair for each level and probabilities for different levels of repair are shown in table below:

  

Repair Category	Repair Cost	Probability
1	$35	0.50
2	$75	0.30
3	$150	0.16
4	$350	0.04

Based on the probabilities given in the two tables and using the random number streams given below, simulate for each of 12 consecutive months the number of breakdowns and the repair cost of each breakdown. Note that for each month you must compute both the number of breakdowns, the repair cost for each breakdown (if any) and the total monthly repair cost as well as the total annual repair cost to answer the following questions.

  
Use the following random numbers in order (from left to right) for the simulation of number of breakdowns per month:

  

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
0.13	0.21	0.08	0.09	0.89	0.26	0.65	0.28	0.97	0.24	0.10	0.90

  
Use the following random numbers in order (from left to right, first row first - as you need them) for the simulation of repair cost for each breakdown.

  

0.19	0.39	0.07	0.42	0.65	0.61	0.85	0.40	0.75	0.73	0.16	0.64
0.38	0.05	0.91	0.97	0.24	0.01	0.27	0.69	0.18	0.06	0.53	0.97

What is the average repair cost in this 12-month simulation?

	A.	$78
	B.	$123.75
	C.	$74.25
	D.	$152.5
	E.	$112.5

Answer 1

Solution :

For the given data , we get

Month	RN	# breakdowns	RN	Cost
1	0.13	1	0.19	$35
2	0.21	1	0.39	$35
3	0.08	0	-	-
4	0.09	0	-	-
5	0.89	4	0.07	$35
			0.42	$35
			0.65	$75
			0.61	$75
6	0.26	1	0.85	$150
7	0.65	2	0.40	$35
			0.75	$75
8	0.28	1	0.73	$75
9	0.97	5	0.16	$35
			0.64	$75
			0.38	$35
			0.05	$35
			0.91	$150
10	0.24	1	0.97	$350
11	0.10	0	-	-
12	0.90	4	0.24	$35
			0.01	$35
			0.27	$35
			0.69	$75
Total				$1,485

Average = 1485 / 12

= $123.75

Therefore, Option B is correct.

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