The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68 percent of the outside diameters lie between what two amounts?
A) 13.5 and 14.5 inches
B) 13.0 and 15.0 inches
C) 13.9 and 14.1 inches
D) 13.8 and 14.2 inches

Question

Quizplus · Accepted Answer

According to the empirical rule, approximately 68% of the data falls within one standard deviation from the mean for any symmetrical, bell-shaped distribution. In this case, one standard deviation is 0.1 inches, so we can find the range of outside diameters that are within one standard deviation of the mean by adding and subtracting 0.1 inches from the mean:
Mean - 1 standard deviation = 14.0 - 0.1 = 13.9 inches
Mean + 1 standard deviation = 14.0 + 0.1 = 14.1 inches
Therefore, about 68% of the outside diameters lie between 13.9 and 14.1 inches, which corresponds to choice C.

The Distribution of a Sample of the Outside Diameters of PVC