(Solved): An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.83 inch. ...

An industrial sewing machine uses ball bearings that are targeted to have a diameter of $$0.83$$ inch. The lower and upper specification limits under which the ball bearing can operate are $$0.82$$ inch (lower) and $$0.84$$ inch (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of $$0.833$$ inch and a standard deviation of $$0.005$$ inch. Suppose a random sample of 25 ball bearings are selected. Complete parts (a) through (e). a. What is the probability that the sample mean is between the target and the population mean of $$0.833$$ ? (Type an integer or decimal rounded to four decimal places as needed.)