A product made by a window manufacturer is constructed 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 glass is discarded due to safety considerations.

c. If the glass thickness is more than 0.075 inch above the mean, it will create installation problems and must be discarded. Calculate the probability that a randomly selected glass will be rejected due to installation concerns.