Question

PVC pipe is manufactured with a mean diameter of 1.0100 inch and a standard deviation of 0.0030 inch. Assuming the diameters follow a normal distribution, find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.0085 inch and less than 1.0121 inch.

Answer 1

0.9153

Explanation:

Computing the z-statistics

`\bf a=(1.0085-1.0100)/(0.0030/√(9))=-1.5\\b=(1.0121-1.0100)/(0.0030/√(9))=2.1`

Now we must compute the area under the Normal Curve with mean 0 and standard deviation 1 between -1.5 and 2.1

P(-1.5 < x < 2.1) = 0.9153

To compute this value we could use a calculator or a spreadsheet.

In Excel or OpenOffice Calc use

NORMSDIST(2.1) - NORMSDIST(-1.5)

(See picture attached)