The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 11.0 inches, and the standard deviation is 2.0 inches. About 68 percent of the outside diameters lie between what two amounts?
8.5 and 12.0 inches
12.0 and 13.0 inches
10.0 and 12.5 inches
9.0 and 13.0 inches
(11.0-2.0, 11.0+ 2.0)
(9.0 , 13.0)
9.0 and 13.0 inches
Thanks again!!
To find the range within which 68 percent of the outside diameters lie, you can use the empirical rule (also known as the 68-95-99.7 rule), which states that for a bell-shaped distribution:
- Approximately 68 percent of the data falls within one standard deviation of the mean.
- Approximately 95 percent of the data falls within two standard deviations of the mean.
- Approximately 99.7 percent of the data falls within three standard deviations of the mean.
Given that the mean is 11.0 inches and the standard deviation is 2.0 inches, we can calculate the range within which 68 percent of the outside diameters lie by adding and subtracting one standard deviation (2.0 inches) from the mean (11.0 inches):
Lower bound: 11.0 inches - 2.0 inches = 9.0 inches
Upper bound: 11.0 inches + 2.0 inches = 13.0 inches
Thus, approximately 68 percent of the outside diameters lie between 9.0 and 13.0 inches.
Therefore, the correct answer is:
- 9.0 and 13.0 inches
To find the range of values that contain approximately 68 percent of the outside diameters, we can use the concept of the empirical rule, also known as the 68-95-99.7 rule.
According to the empirical rule, for a bell-shaped distribution:
- Approximately 68 percent of the data falls within one standard deviation of the mean.
- Approximately 95 percent of the data falls within two standard deviations of the mean.
- Approximately 99.7 percent of the data falls within three standard deviations of the mean.
In this case, since the mean is 11.0 inches and the standard deviation is 2.0 inches, one standard deviation below the mean would be 11.0 - 2.0 = 9.0 inches, and one standard deviation above the mean would be 11.0 + 2.0 = 13.0 inches.
Therefore, approximately 68 percent of the outside diameters would lie between 9.0 and 13.0 inches.
So, the correct answer is "9.0 and 13.0 inches".