Question: When the widget-making machine at WidgetCo is working properly, the widgets it produces are normally distributed with mean = 3 in . and standard deviation

When the widget-making machine at WidgetCo is working properly, the widgets it produces are normally distributed with mean = 3 in. and standard deviation = .1 in. Every day, the quality-control inspector takes a simple random sample of 25 widgets. He will shut down the machine for an overhaul if the mean length of the widgets in the sample is not between 2.95 in. and 3.05 in.

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A) Assuming the machine is working properly (i.e., = 3), what is the probability that the mean length of the widgets in the sample is between 2.95 and 3.05 in.?

B) What is the probability that the mean length of the widgets in the sample is not between 2.95 and 3.05 in.? (This is the probability that the machine will be shut down for an overhaul, even though it is running properly.)

C) Suppose the machine goes out of control and starts producing widgets with a mean length = 3.018 in.

Repeat the calculation in a). (This result gives the probability that the machine will not be shut down for an overhaul, even though the widgets being produced are too long.

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