Refer to given Exercise. Suppose that the machine is considered to be out of statistical control if the average diameter of a sample of 36 bearings is less than 34.75 mm or greater than 35.25 mm.
(a) If the true mean diameter of all bearings produced is 35 mm, what is the probability of the test indicating that the machine is out of control?
(b) Suppose that the setting of the machine is accidentally changed such that the mean diameter of all bearings produced is 35.05 mm. What is the probability of the test indicating that the machine is in statistical control?
Exercise
The diameter of bearings is known to have a mean of 35 mm with a standard deviation of 0.5 mm. A random sample of 36 bearings is selected. What is the probability that the average diameter of these selected bearings will be between 34.95 and 35.18 mm?