According to recent research, the mean height for women in the U.S. is 63.7 inches (which you
Already knew, right?), and the standard deviation is 2.7 inches. The normal graph below is marked
With the mean and heights that are one and two standard deviations above and below the mean. Make an educated guess on the percentage of total shaded area between 58.3 and 69.1 inches.
A)about 99%
B)about 95%
C)about 48%
D)about 34%

Question

According to recent research, the mean height for women in the U.S. is 63.7 inches (which you
Already knew, right?), and the standard deviation is 2.7 inches. The normal graph below is marked
With the mean and heights that are one and two standard deviations above and below the mean.  Make an educated guess on the percentage of total shaded area between 58.3 and 69.1 inches.
A)about 99% 
B)about 95% 
C)about 48% 
D)about 34%

Quizplus · Accepted Answer

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean and approximately 95% falls within two standard deviations of the mean.

So, the interval from 58.3 to 69.1 inches is within two standard deviations of the mean. Therefore, we can estimate that approximately 95% of the total shaded area is between these two heights. According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean. Since we are looking for the percentage of area between 58.3 and 69.1 inches, which is within two standard deviations of the mean, the best choice is B, about 95%.

According to Recent Research, the Mean Height for Women in the U.S