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The average 20-29-year-old man is 153 pounds with a standard deviation of 9 pounds, while a 20-29-year-old woman is 125 pounds with a standard deviation of 7 pounds. Who is relatively "heavier": a 168-pound man or a 137-pound woman?

Answer :

Final answer:

Relative heaviness is determined by comparing 'z-scores', or how many standard deviations an individual is from the average of their group. The 137 pound woman, who is 1.71 standard deviations above the average, is relatively heavier than the 168 pound man, who is 1.67 standard deviations above the average.

Explanation:

In order to answer who is relatively "heavier", a 168 pound man or a 137 pound woman, we have to compare how many standard deviations the individuals are from their respective averages. This information is called a 'z-score'.

For the man, we calculate: Z = (168-153)/9 = 1.67. This means the man is 1.67 standard deviations heavier than the average man.

For the woman, we find: Z = (137-125)/7 = 1.71. So the woman is 1.71 standard deviations heavier than the average woman.

Based on these z-scores, this woman is relatively heavier than the man because her weight is further from the average weight of her group.

Learn more about z-score here:

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