Question

In: Statistics and Probability

One of the large photocopiers used by a printing company has a number of special functions...

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


On which month, the largest number of repairs occurred?
  

A.

September

B.

July

C.

May

D.

December

E.

October

What was the total monthly repair cost in May?

A.

$75

B.

$300

C.

$140

D.

$220

E.

$35

What is the annual total cost of repairs in this 12-month simulation?   
a) $1845 b) $1485 c) $1570 d) $2250 e) $1480

A.

$1845

B.

$1480

C.

$1485

D.

$2250

E.

$1570

Solutions

Expert Solution

Answer:

On which month, the largest number of repairs occurred?

ans; May

What was the total monthly repair cost in May?

Option B is Correct

What is the annual total cost of repairs in this 12-month simulation?   

Simulation model:

Result:

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

Option C is Correct

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