Asked by lauren campbell on Jul 12, 2024
Verified
If the average height for adult men in the United States is approximately normally distributed with mean 70 inches and the standard deviation about 3 inches, it follows from the 68-95-99.7 rule that _____.
A) 68 percent of the men in the U.S. are between 64 inches and 67 inches in height
B) about 95 percent of the adult men in the U.S. are between 73 inches and 76 inches tall
C) 99.7 percent of the men in the U.S. are between 61 inches and 79 inches tall
D) 95 percent of men in the U.S. are between 61 inches and 64 inches tall
E) almost 99.7 percent of the men in the U.S. are between 61 inches and 76 inches tall
68-95-99.7 Rule
A statistical rule stating that in a normal distribution, about 68% of observed values fall within one standard deviation, 95% within two, and 99.7% within three standard deviations of the mean.
Normally Distributed
Describes a statistical distribution where data points are symmetrically distributed around the mean, forming a bell-shaped curve.
Standard Deviation
A statistical measure that represents the amount of variation or dispersion from the average in a set of data.
- Comprehend the function of statistical distributions, particularly the normal distribution, in evaluating and guaranteeing quality.
Verified Answer
GQ
Guillermo QuintanillaJul 16, 2024
Final Answer :
C
Explanation :
The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. Given a mean of 70 inches and a standard deviation of 3 inches, 99.7% of men would fall within three standard deviations of the mean, which calculates to between 61 inches (70-3*3) and 79 inches (70+3*3).
Learning Objectives
- Comprehend the function of statistical distributions, particularly the normal distribution, in evaluating and guaranteeing quality.