Normal Distribution of PVC Gas Pipe Outside Diameters: Mean, Standard Deviation, and Percentile Ranges

What Are the Percentile Ranges for PVC Gas Pipe Outside Diameters?

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Question

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

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A

Approximately 68% of observations will lie within plus and minus one standard deviation of the mean.

To solve this problem, we can use the properties of the normal distribution. According to the empirical rule (also known as the 68-95-99.7 rule), in a symmetrical, bell-shaped distribution:

  • Approximately 68% of the data falls within one standard deviation of the mean.
  • Approximately 95% of the data falls within two standard deviations of the mean.
  • Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean outside diameter of the sample is 14.0 inches and the standard deviation is 0.1 inches, we can apply the empirical rule to find the range within which about 68% of the outside diameters lie.

The range can be calculated as follows:

Lower limit = Mean - 1 standard deviation Upper limit = Mean + 1 standard deviation

Lower limit = 14.0 - 0.1 = 13.9 inches Upper limit = 14.0 + 0.1 = 14.1 inches

Therefore, about 68% of the outside diameters lie between 13.9 and 14.1 inches.

Based on the available options, the correct answer is:

A. 13.9 and 14.1 inches

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