An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearings can operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.753 inch and a standard deviation of 0.004 inch. What is the probability that a ball bearing is
a. Between the target and the actual mean?
b. Between the lower specification limit and the target?
c. Above the upper specification limit?
d. Below the lower specification limit?
e. Of all the ball bearings, 93% of the diameters are greater than what value? Discuss.