# Solved (Free): Of two persons on a reducing diet, the first belongs to an age group for which the mean weight is 142 pounds with a standard deviation

#### ByDr. Raju Chaudhari

Mar 29, 2021

Of two persons on a reducing diet, the first belongs to an age group for which the mean weight is 142 pounds with a standard deviation of 15 pounds, and the second belongs to an age group for which the mean weight is 138 pounds with a standard deviation of 13 pounds. If their respective weights are 161 pounds and 154 pounds, which of the two is more seriously overweight for his or her age group? (use z-scores and round to the hundredths, if necessary)

#### Solution

Let $X$ = weight of first group. $X\sim N(142,15^2)$.

For first group, the mean weight is $\mu = 142$ and standard deviation is $\sigma =15$.

The $Z$ score formula is $Z= \dfrac{X-\mu}{\sigma}$.

Weight of a person from first age group is $161$.

His/her z score for weight is

\begin{aligned} Z&= \frac{161-142}{15}\ &= 1.27. \end{aligned}

Let $Y$ = Weight of second group. Given that $Y\sim N(138, 13^2)$.

The Z-score formula is $Z= \dfrac{Y-\mu}{\sigma}$.

For second group, the mean weight is $\mu = 138$ and standard deviation is $\sigma =13$.

Weight of a person from second age group is $154$.

His/her z score for weight is

 \begin{aligned} Z&= \frac{154-138}{13}\\ &= 1.23 \end{aligned}

Because the z-score (1.27) of a person from first age group is larger than the z-score (1.23) of a person from second age group, a person from first age group is more seriously overweight for his or her age group.