Question

use the data on the right to find the distance of each boys height from the mean.

distance from mean: \\(x - \mu\\)

distance of joses height from mean: in.
distance of jamals height from mean: in.

jose and jamal are friends.

jose is 51\ tall and 7 years old. jamal is 55.7\ tall and 12 years old.

heights of boys at a given age are normally distributed.

age	mean	standard deviation
12 years	58 inches	2.3 inches

Explanation:

Identify given values and formula

Using the Z-Score Formula knowledge point
The problem defines the distance from the mean as:

$$ \text{Distance from mean} = x - \mu $$

where:

• \(x\) is the individual value (height).
• \(\mu\) is the mean height for the corresponding age group.

From the text and table:

• Jose: age = \(7\text{ years}\), height \(x_1 = 51\text{ in.}\), mean \(\mu_1 = 49\text{ in.}\)
• Jamal: age = \(12\text{ years}\), height \(x_2 = 55.7\text{ in.}\), mean \(\mu_2 = 58\text{ in.}\)

Calculate Jose's distance from the mean

Using the Z-Score Formula knowledge point

$$ x_1 - \mu_1 = 51 - 49 = 2 $$

Calculate Jamal's distance from the mean

Using the Z-Score Formula knowledge point

$$ x_2 - \mu_2 = 55.7 - 58 = -2.3 $$

Answer:

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

Distance from mean: \(x - \mu\)

Distance of Jose's height from mean: <blank>2</blank> in.
Distance of Jamal's height from mean: <blank>-2.3</blank> in.