The Comfort Widget Company makes several different sized widgets. The smallest widget the company manufactures has a mean diameter of 1.5 inches with a standard deviation of .15 inches. The distribution of measurements for this widget's diameter is approximately normal.
a: What is the probability that a randomly selected single widget will have a diameter greater than 1.7 inches?
b: What is the probability that a randomly selected single widget will have a diameter between 1.4 and 2.2 inches?
c: Management will become concerned if more than 10% of the widgets from a particular machine are out of tolerance. Calculate the 5th percentile and the 95th percentile to find the measurements you would use to evaluate management's concern.