Question

1. Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.00mm, but shafts with diameters between 21.99m and 22.01mm are acceptable. Suppose that the manufacturing process yields shafts with diameters normally distributed, with a mean of 22.00 mm and a standard deviation of 0.005 mm.
   1. For this process, what is the proportion of shafts with a diameter between 21. 99mm and 22.00mm? What is the probability that a shaft is acceptable?
   2. Let X be the number of acceptable shafts in the next 100 shafts manufactured. What is the distribution of X? What is the probability that in these 100 shafts, at most 2 of them are unacceptable?
   3. Let Y be number of shafts produced since the start of the day until one unacceptable shaft is found, what is the distribution of Y? What is the probability that at least 50 acceptable shafts have been produced before the first unacceptable one is found?

Answer 1

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