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Use the data on the right to find the distance of each boy's height from the mean.

Distance from mean: [tex]x - \mu[/tex]

- Distance of Jose's height from mean: [tex]\square[/tex] in.
- Distance of Jamal's height from mean: [tex]\square[/tex]

Jose and Jamal are friends.
Jose is [tex]51^{\prime \prime}[/tex] tall and 7 years old.
Jamal is [tex]55.7^{\prime \prime}[/tex] tall and 12 years old.

Heights of boys at a given age are normally distributed.

\begin{tabular}{|c|c|c|}
\hline Age & Mean & \begin{tabular}{c}
Standard \\
Deviation
\end{tabular} \\
\hline 7 years & 49 inches & 2 inches \\
\hline 12 years & 58 inches & 2.3 inches \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To find the distance of each boy's height from the mean, we use the following formula for the distance from the mean:
[tex]\[ \text{Distance from mean} = x - \mu \][/tex]
where [tex]\( x \)[/tex] is the actual height of the boy, and [tex]\( \mu \)[/tex] is the mean height for boys of his age.

Given the data:
- Jose is 51 inches tall and 7 years old.
- Jamal is 55.7 inches tall and 12 years old.

From the table:
- For 7 years old, the mean height ([tex]\( \mu \)[/tex]) is 49 inches.
- For 12 years old, the mean height ([tex]\( \mu \)[/tex]) is 58 inches.

We will calculate the distances as follows:

### Distance of Jose's height from the mean
[tex]\[ \text{Distance of Jose's height from mean} = 51 - 49 = 2 \text{ inches} \][/tex]

### Distance of Jamal's height from the mean
[tex]\[ \text{Distance of Jamal's height from mean} = 55.7 - 58 = -2.3 \text{ inches} \][/tex]

The distances are:

- Distance of Jose's height from mean: [tex]\( 2 \)[/tex] inches
- Distance of Jamal's height from mean: [tex]\( -2.3 \)[/tex] inches

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