A machine operation produces widgets whose diameters are nor

A machine operation produces widgets whose diameters are normally distributed, with a mean of 4.97 inches and a standard deviation of 0.06 inches. Suppose that specifications specifications require that the widget diameter be 5.00 inches plus or minus 0.12 inches (that is, between 4.88 and 5.12 inches). What proportion of the production will be unacceptable? Suppose 25 widgets are independently and randomly selected from the production process. What is the probability that exactly 2 of the 25 will be unacceptable? A quality control inspector selects 25 widgets from the production independently and at random. If the average diameter of the selected widgets is within 0.06 inches of 5.00 inches (that is, between 4.94 and 5.06 inches), the production process is allowed to continue. However, if the average diameter of the selected widgets is not within 0.06 inches of 5.00 inches, the production process is stopped and the machine is checked. What is the probability that the production process will be stopped after examining a random sample of 25 widgets?

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