Question

The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts?

Answer 1

13.9 inches, 14.1 inches

Explanation:

The empirical rule tells you 68% of the distribution lies within 1 standard deviation of the mean:

14.0 ± 0.1 = [13.9, 14.1]

About 68% of outside diameters lie between 13.9 inches and 14.1 inches.

Answer 2

Between 13.9 and 14.1 inches.

Explanation:

This approximates to a normal distribution so 68% of the values will be within 1 standard deviation either side of the mean.

So about 68% of the diameters will lie between 13.9 and 14.1 inches.