Probability Distribution Case
Chapter 6
Continuous Probability Distributions
Case Problem: Specialty Toys
1. Information provided by the forecaster
At x = 30,000,
[pic]
[pic]
Normal distribution [pic] [pic]
2. @ 15,000
[pic]
P(stockout) = 1 - .1635 = .8365
@ 18,000
[pic]
P(stockout) = 1 - .3483 = .6517
@ 24,000
[pic]
P(stockout) = 1 - .7823 = .2177
@ 28,000
[pic]
P(stockout) = 1 - .9418 = .0582
3. Profit projections for the order quantities under the 3 scenarios are computed below:
Order Quantity: 15,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |240,000 |240,000 |25,000 | 25,000 |
|20,000 |240,000 |360,000 | 0 |120,000 |
|30,000 |240,000 |360,000 | 0 |120,000 |
Order Quantity: 18,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |288,000 |240,000 |40,000 | -8,000 |
|20,000 |288,000 |432,000 | 0 |144,000 |
|30,000 |288,000 |432,000 | 0 |144,000 |
Order Quantity: 24,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |384,000 |240,000 |70,000 | -74,000 |
|20,000 |384,000 |480,000 |20,000 |116,000 |
|30,000 |384,000
Continuous Probability Distributions
Case Problem: Specialty Toys
1. Information provided by the forecaster
At x = 30,000,
[pic]
[pic]
Normal distribution [pic] [pic]
2. @ 15,000
[pic]
P(stockout) = 1 - .1635 = .8365
@ 18,000
[pic]
P(stockout) = 1 - .3483 = .6517
@ 24,000
[pic]
P(stockout) = 1 - .7823 = .2177
@ 28,000
[pic]
P(stockout) = 1 - .9418 = .0582
3. Profit projections for the order quantities under the 3 scenarios are computed below:
Order Quantity: 15,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |240,000 |240,000 |25,000 | 25,000 |
|20,000 |240,000 |360,000 | 0 |120,000 |
|30,000 |240,000 |360,000 | 0 |120,000 |
Order Quantity: 18,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |288,000 |240,000 |40,000 | -8,000 |
|20,000 |288,000 |432,000 | 0 |144,000 |
|30,000 |288,000 |432,000 | 0 |144,000 |
Order Quantity: 24,000
| | |Sales | |
|Unit Sales |Total Cost |at $24 |at $5 |Profit |
|10,000 |384,000 |240,000 |70,000 | -74,000 |
|20,000 |384,000 |480,000 |20,000 |116,000 |
|30,000 |384,000