# 0117 0083 0025 0007 0002 this is still quite unlikely

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0117 (.0083 + .0025 + .0007 + .0002). This is still quite unlikely to happen by chance. If seven complaints are actually logged, then managers would have to strongly consider the possibility that the average rate of 2.4 complaints has increased. This is, as has been stated, unacceptable to management. 3. This is a hypergeometric problem with: N = 52, n = 10, A = 18 (customer satisfaction), and x = 7 The probability is computed as: 10 52 3 34 7 18 C C C = .0120 The probability that seven out of the ten successful products were created for customer service when only eighteen of the fifty-two original products were created for customer service is about 1% (.012). Since this is unlikely to happen by chance, it is likely that there is something inherently more successful about creating a product for customer service reasons than for revenue growth.

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Case Notes 13 Chapter 6 Mercedes Goes after Younger Buyers 1. Prob( x > 42,000 μ = 43,215 and σ = 2981): 2981 215 , 43 000 , 42 - = - = σ μ x z = -0.41 From Table A.5, the area for z = -0.41 is .1591. Prob( x > 42,000) = .5000 + .1591 = .6591 = 65.91% Almost 66% of Mercedes dealers would be priced out of competition with this BMW model. Prob ( x > 43,215 μ = 34,990 and σ = 2367): 2367 990 , 34 215 , 43 - = - = σ μ x z = 3.47 From Table A.5, the area for z = 3.47 is .4997. Prob( x > 43,215) = .5000 - .4997 = .0003 = 0.03% Virtually none of the BMW dealers are pricing the 328 ci more than the average price of the Mercedes CLK320. Prob( x < 34,990 μ = 43,215 and σ = 2981): 2981 215 , 43 990 , 34 - = - = σ μ x z = -2.76 From Table A.5, the area for z = -2.76 is .4971. Prob( x < 34,990) = .5000 - .4971 = .0029 = 0.29% About .3% of the Mercedes dealers are pricing CLK320 less than the average price of the BMW 320 ci . Prob( x < 37,059 μ = 43,215 and σ = 2981):
Case Notes 14 2981 215 , 43 059 , 37 - = - = σ μ x z = -2.07 From Table A.5, the area for z = -2.07 is .4808. Prob(X < 37,059) = .5000 - .4808 = .0192 = 1.92% Less than 2% of the Mercedes dealers price the CLK320 less than \$37,059. Conclusion: There is little overlap in the prices of the two cars and it could be concluded that they are not really competing with each other pricewise. 2. CLK: a = 24 b = 34 x 1 = 26 x 2 = 30 Prob. = 24 34 26 30 - - = .4 = 40% 328is: a = 25 b = 35 x 1 = 26 x 2 = 30 Prob. = 25 35 26 30 - - = .4 = 40% The same proportion of 328is cars fall into this category (26-30 mpg). However, an examination of the end points of the mileage distributions of each car reveals that the upper end for 328’s is 1 mpg. higher than for the 328is’s and the lower end for CLK’s is 1 mpg. lower. Both cars have very close gas mileage figures. Each car more than 30 mpg.: For CLK: Prob. = 24 34 30 34 - - = .4 = 40% For 328is: Prob. = 25 35 30 35 - - = .5 = 50% A higher proportion of 328’s are in the more than 30 mpg. category than CLK’s.

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Case Notes 15 3. λ = 1.37 cars/3 hours, μ = 1/1.37 = .73 of 3 hours = 2.19 hours For 1 hour: 1 hour = .333 of 3 hours. x 0 = 0.333. The cumulative probability of this time interval is .3663. This means that there is a 36.63% chance that there will be less than one hour between sales. For 12 hours: 12 hours = 4 times 3 hours. x 0 = 4. The cumulative probability for this time interval is . 9958 meaning that there is a 99.58% chance that there will be less than 12 hours between sales. The complement of this is that there is a 1 - .9958 = .0042 = 0.42% chance that there will be more than 12 hours between sales.
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