Problem 11E

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 rods fail to meet the specifications?

(b) Assume that the probability density function is f (x) = 2 for an interval of length 0.5 meters. Over what value should the density be centered to achieve the greatest proportion of rods within specifications?

Solution:

Step 1 of 3:

It is given that X denotes the length of metal rod and has the density function f(x)=2;2.3<x<2.8 meters.

Using this we need to find the required values.