Probability Distribution Case

Chapter 6
Continuous Probability Distributions

Case Problem: Specialty Toys

1. Information provided by the forecaster

At x = 30,000,

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Normal distribution [pic] [pic]

2. @ 15,000

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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