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# TP%2311_f08 - CE 3102 Fall 2008 Thought Problem 11...

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CE 3102 Fall 2008 Thought Problem 11 Introducing the Normal Distribution An automobile manufacturer is considering recalling an automobile model to correct a manufacturing defect. Based on a sample of inspected vehicles, it has been determined that the defect occurs randomly, and that about 15% of the automobile contain the defect. If all 10000 of the manufactured vehicles are recalled, what is the probability that at least 1600 have defects?

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CE 3102 Fall 2008 Thought Problem 11 Instructor’s Partial Solution Let X denote the number of defective automobiles. A natural model for this problem would that X is a binomial random variable, with p=0.15, and n=10000. The probability of obtaining at least 1600 defective vehicles would then be = - - - = < - = 1599 0 10000 ) 85 (. ) 15 (. )! 10000 ( ! ! 10000 1 ) 1600 ( 1 ) 1600 ( k k k k k X P X P As with our road accident model, this is a computation that is doable (on a computer) but non-trivial, and was definitely outside the realm of possibility back in the 18 th century.
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