A machine produces bearings with mean diameter 3.00 inches

Solution 29SE

Step1 of 3:

Let us consider a random variable “X” it presents the number of bearings produced by a machine. Bearings with diameters in excess of 3.02 inches or less than 2.98 inches will fail to meet quality specifications. A random variable “X” follows normal distribution with mean and standard deviation

That is XN() 

XN()

Here our goal is:

a). We need to check what fraction of this machine’s production will fail to meet specifications.

b). We need to write assumptions for concerning the distribution of bearing diameters in order to answer this question.

Step2 of 3:

a).

Consider,