# The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. Is it reasonable to believe that the distribution of body weights for women aged 20 to 29 is approximately Normal? Explain your answer.

The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. Is it reasonable to believe that the distribution of body weights for women aged 20 to 29 is approximately Normal? Explain your answer.
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Peyton Cox
Given:
Mean
Median​
=141.7
=133.2​
We note that the mean is much larger than the median.
Since the mean is not resistant and the median is resistant, the mean is influenced more by unusually large/small data values. In this case, the mean is larger than the median, which indicates that there are unusually large data values and thus the distribution is skewed to the right.
However, the Normal distribution is symmetric and thus the distribution of body weights does not appear approximately Normal.
Result:
No, because the distribution appears to be skewed to the right.