SBE10 CP06 - Chapter 6 Continuous Probability Distributions...

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Chapter 6 Continuous Probability Distributions Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30,000, 30,000 20,000 1.96 x z μ σ σ - - = = = 30,000 20,000 5102 1.96 σ - = = Normal distribution 20,000 μ = 5102 σ = 2. @ 15,000 15,000 20,000 0.98 5102 z - = = - P(stockout) = 0.3365 + 0.5000 = 0.8365 @ 18,000 18,000 20,000 0.39 5102 z - = = - P(stockout) = 0.1517 + 0.5000 = 0.6517 @ 24,000 24,000 20,000 0.78 5102 z - = = P(stockout) = 0.5000 - 0.2823 = 0.2177 CP - 18 20,000 . 025 10,000 30,000 . 025 . 95
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Chapter 6 Continuous Probability Distributions @ 28,000 28,000 20,000 1.57 5102 z - = = P(stockout) = 0.5000 - 0.4418 = 0.0582 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 30,000 384,000 576,000 0 192,000 Order Quantity: 28,000 Sales Unit Sales Total Cost at $24 at $5 Profit 10,000 448,000 240,000 90,000 -118,000 20,000 448,000 480,000 40,000 72,000 30,000 448,000 672,000 0 224,000 CP - 19
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Chapter 6 Continuous Probability Distributions 4. We need to find an order quantity that cuts off an area of .70 in the lower tail of the normal curve for
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