The probability density function of the length of a metal rod is f(x) =2 for 2.3 < x < 2.8 meters.
(a) If the specifications for this process are from 2.25 to 2.75 meters, what proportion of the bars fails to meet the specifications?
(b) Assume that the probability density function is f(x) = 2 an interval of length 0.5 meters. Over what value the density should be centered to achieve the greatest proportion of bars within specifications?