please solve this part: As we’ve previously seen, equations describing situation

ID: 3775961 • Letter: P

Question

please solve this part:

As we’ve previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren’t necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function.
Consider the following total profit function:
PT = nPv
Where PT is the total profit, n is the number of vehicles sold and Pv is the profit per vehicle in a simple calculation made when figuring the profit made from selling a car..
PART A
Compute 5 iterations of a Monte Carlo simulation given the following information:
n follows a uniform distribution with minimum of 1 and maximum 10
Pv follows a normal distribution with a mean of $5500 and a standard deviation of $1000
Number of bins: 10
Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I’d give you a break . If you’d like to compute 10,000 iterations by hand for extra credit, go ahead…
i.) What are the ranges for the 10 bins?
ii.) Fill in the table below:
Parameter
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Iteration 5
n
3
7
8
4
5
Pv
$3200
$4500
$5500
$7500
$2500 PT Bin # $ Range
iii.) Fill in the frequency of occurrences of each bin:
1:
2:
3:
4:
5:
6:
7:
8:
9:
10

Explanation / Answer

1)n : nmin = 1 , nmax = 10

Pv: Pvmin = $1000, Pvmax = $7,000

Ptmin = nmin * Pvmin = $1000

Ptmax = nmax * Pvmax = $70,000

Range/Bin = (70000 – 1000)/10 = 6,900

Bin 1: 1000 – 7900

Bin 2: 7901 – 14800

Bin 3: 14801 – 21700

Bin 4: 21701 – 28600

Bin 5: 28601 – 35500

Bin 6: 35501 – 42400

Bin 7: 42401 – 49300

Bin 8: 49301 – 56200

Bin 9: 56201 – 63100

Bin 10: 63101 – 70000

Parameter

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Iteration 5

$3100

$4500

$3400

$6500

$2200

$6200

$31500

$30600

$26000

$11000

Bin #

$ Range

1000 – 7.9k

28601 – 35.5k

28601 - 35.5k

21701 – 28.6k

7901 – 14.8k

3) 1.1

2.1

3.0

4.1

5.2

6.0

7.0

8.0

9.0

10.0