The probability density function for the length of a metal r

The probability density function for the length of a metal rod is f(y) = 4 for 3.5 < y < 3.75 meters.

(a) If the specifications for this process are that the rods should be 3.45 - 3.7 meters long, what proportion of rods fails to meet the specifications?

(b) Assume that the probability density function is f(y) = 4 for an interval of length 0.25 meters. Over what value should the density be centered to achieve the greatest proportion of bars within specifications?

(c) For the original pdf, find the mean and s.d. of the length of a randomly-selected rod.

Solution