Quality control. Refer to Exercise 6.84. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean to decide whether the process is in control

(i.e., whether it is producing bearings with a mean diameter of .5 inch). The machine will be considered out of control if the mean of the sample of n = 36.

Diameters is less than .5025 inch or larger than .5045 inch. If the true mean diameter of the bearings produced by the machine is .505 inch, what is the approximate probability that the test will imply that the process is out of control?