Pvc pipe is manufactured with a mean diameter of 1.01 inch and a standard deviation of 0.003 inch. the diameters are known to be normally distributed. find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.

about 82%

Step-by-step explanation:

The distribution of sample means has a standard deviation that is the pipe standard deviation divided by the square root of the sample size. Thus, the standard deviation of the sample mean is 0.003/√9 = 0.001.

Then the limits on sample mean are 1.010 - 1×0.001 = 1.009 and 1.010 +2×0.001 = 1.012. The proportion of the normal distribution that lies between -1 and +2 standard deviations is about 81.9%.