ENME 392 - Homework 3 Solutions - Sp12

ENME 392 - Homework 3 Solutions - Sp12 - ENME392 Spring...

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ENME392 Spring 2012 Homework 3 Solutions Total number of points: 100 Assignment: 1. Chapter 2: 2.75 (Edition 8) / 2.71 (Edition 9) (6 pts) P(meets spec) = 0.95 P(too light) = 0.002 cost $20, sold $25 (a) P(too heavy) = 1 – 0.95 – 0.002 = 0.048 (b) Profit on 10k perfect packages? 10,000 * $5 =$50,000 (c) Defective packages are worthless. Profit? Loss = 0.05 *10,000 * $20 = $10,000 Profit on good ones = 0.95 * 10,000 * $5 = $47,500 Profit – loss = $37,500 Profit is reduced from $50,000 for 100% perfect by $12,500 by the 5% bad ones b the 5% bad ones have more than a 5% impact on profit! 2. Chapter 2: 2.98 (Edition 8) / 2.92 (Edition 9) (2 pts) gG±²±³´µ ¶·¸¹±º = gG» ∩ G¼ ∪ ½º ∩ ¾º = gG»º × gG¼ ∪ ½º × gG¾º gG±²±³´µ ¶·¸¹±º = gG»º × [gG¼º + gG½º − gG¼ ∩ ½º] × gG¾º gG±²±³´µ ¶·¸¹±º = gG»º × [gG¼º + gG½º − gG¼º × gG½º] × gG¾º gG±²±³´µ ¶·¸¹±º = .95 × G. 7 + .8 − .7 × .8º × .9 = .8037 3. Chapter 2: 2.99 (Edition 8) / 2.93 (Edition 9) (4 pts) a) gG±²±³´µ ¶·¸¹±º = g¿G» ∩ ¼º ∪ G½ ∩ ¾ ∩ ÀºÁ = gG» ∩ ¼º + gG½ ∩ ¾ ∩ Àº − gG» ∩ ¼ ∩ ½ ∩ ¾ ∩ Àº gG» ∩ ¼º = gG»º × gG¼º = .7 × .7 = .49 gG½ ∩ ¾ ∩ Àº = gG½º × gG¾º × gGÀº = .8 × .8 × .8 = .512 gG» ∩ ¼ ∩ ½ ∩ ¾ ∩ Àº = gG»º × gG¼º × gG½º × gG¾º × gGÀº = .7Â × .8à = .25088 gG±²±³´µ ¶·¸¹±º = .49 + .512 − .25088 = .75112
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b) gG± ² /³´³µ¶· ¸¹º»³¼ = ½G¾ ¿ ∩ÀÁÀÂÃÄ ÅÆÇÈÀ¼ ½GÀÁÀÂÃÄ ÅÆÇÈÀ¼ = ½G¾ ¿ ∩É∩Ê∩˼ ½GÀÁÀÂÃÄ ÅÆÇÈÀ¼ = gG± ² /³´³µ¶· ¸¹º»³¼ = gG±′¼ × gG̼ × gGͼ × gGμ gG³´³µ¶· ¸¹º»³¼ = [1 − gG±¼] × gG̼ × gGͼ × gGμ gG³´³µ¶· ¸¹º»³¼ gG± ² /³´³µ¶· ¸¹º»³¼ = G1 − .7¼ × .8Ï . 75112 = .2045 4. Chapter 2: 2.110 (Edition 8) / 2.104 (Edition 9) + (c) at least 3 of her next 4 patients are allergic to weed? (d) not more than 1 of her next 4 patients is allergic to weed? (e) at least 1 of her next 4 patients are allergic to weed? (10 pts)
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ENME 392 - Homework 3 Solutions - Sp12 - ENME392 Spring...

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