One of the products of Pittsburg Plate Glass Industries (PPG) is laminated safety glass. It is made up of two pieces of glass 0.125 inch thick, with a thin layer of vinyl sandwiched between them. The average thickness of the laminated safety glass is 0.25 inch. The thickness of the glass does not vary from the mean by more than 0.10 inch. Assume the thickness of the glass has a uniform distribution.
a. Provide the density for this uniform distribution.
b. If the glass has a thickness that is more than 0.05 inch below the mean, it must be discarded for safety considerations. Determine the probability that a randomly selected automobile glass is discarded due to safety considerations.
c. If the glass is more than 0.075 above the mean, it will create installation problems and must be discarded. Calculate the probability that a randomly selected automobile glass will be rejected due to installation concerns.
d. Given that a randomly selected automobile glass is not rejected for safety considerations, determine the probability that it will be rejected for installation concerns.