Question

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 135.7 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? no, because the median is not the same as the mean. it might be depending on the values of the maximum and minimum. no, because the median is not midway between the first and third quartiles. yes. if heights are approximately normal, so are weights.

Explanation:

In a normal distribution, the mean, median, and mode are equal. Also, the median is midway between the first and third quartiles (i.e., \(Q_2=\frac{Q_1 + Q_3}{2}\)). Here, mean \(= 135.7\), median \(=133.2\) (so mean \(
eq\) median). Also, \(\frac{Q_1+Q_3}{2}=\frac{118.3 + 157.3}{2}=\frac{275.6}{2}=137.8
eq133.2\) (median).

Answer:

No, because the median is not midway between the first and third quartiles.