You are preparing some sweet potato pie for your annual Thanksgiving feast. The
ID: 3200498 • Letter: Y
Question
You are preparing some sweet potato pie for your annual Thanksgiving feast. The store sells sweet potatoes in packages of 6. From prior experience you have found that the package will contain 0 spoiled sweet potatoes about 65% of the time, 1 spoiled sweet potato 25% of the time and 2 spoiled sweet potatoes the rest of the time. Conduct a simulation to estimate the number of packages of sweet potatoes you need to purchase to have three dozen (36) unspoiled sweet potatoes.
Part 1 of 3: B Describe in detail and in paragraph form how you will use the random numbers provided from a random number table (in part 2) to conduct 4 trials of this simulation. Be sure to include all of the first four steps of a simulation. Steps 5 and 6 are part 2 and step 7 are part 3 of this question. 1. Identify the component to be repeated. 2. Explain how you will model the outcome. 3. Explain in detail how you will simulate the trial. 4. State clearly what the response variable is.
Part 2: Using the data from our random number table below, carry out your simulation from part 1. For each of the 4 trials, show the detailed outcome (package by package) and specify your overall results (total number of packages in that trial). Then show work for analyzing the response variable. This is steps 5 and 6 of a simulation: 5. Run several trials 6. Analyze the response variable.
1 80942 52582 47134 77433
2 35632 19882 11904 52618
3 13306 33137 53969 38738
4 35650 01622 43643 24796
Part 3: Complete your simulation by stating your conclusion to the simulation in context. (step 7).
Explanation / Answer
Solution
Simulation Process
Step 1: Take 2-digit random numbers starting from any random point of the table.
Step 2:
a) If the picked random number is 00 to 64 (both inclusive), take that the package has 0 spoiled sweet potato and so all the 6 in the package are good.
b) If the picked random number is 65 to 89 (both inclusive), take that the package has 1 spoiled sweet potato and so 5 in the package are good.
c) If the picked random number is 90 to 99 (both inclusive), take that the package has 2 spoiled sweet potato and so 4 in the package are good.
Step 3: Keep repeating above steps, till total number of unspoiled potatoes in the packages is 36.
Step 4: Actual simulation with the given random numbers
80942 52582 47134 77433
2 35632 19882 11904 52618
3 13306 33137 53969 38738
4 35650 01622 43643 24796
We start from col 6 row1. All steps are represented in the following table:
Serial No
Random number
Number of spoiled ones in the package
Number of un-spoiled ones in the package
Cumulative number of un-spoiled ones in the package
Remarks, if any
1
52
0
6
6
2
58
0
6
12
3
24
0
6
18
4
71
1
5
23
5
34
0
6
29
6
77
1
5
34
7
43
0
6
40
Since total number of unspoiled sweet potatoes has just exceeded the stipulated 36, simulation is stopped.
This simulation trial took 7 steps to achieve the desired result. So, 7 packages are required.
Serial No
Random number
Number of spoiled ones in the package
Number of un-spoiled ones in the package
Cumulative number of un-spoiled ones in the package
Remarks, if any
1
52
0
6
6
2
58
0
6
12
3
24
0
6
18
4
71
1
5
23
5
34
0
6
29
6
77
1
5
34
7
43
0
6
40
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