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: 2 in.
distance of jamals height from mean: -2.3 in.

how many standard deviations is joses height from the mean height for 7-year-olds?
how many standard deviations is jamals height from the mean height for 12-year-olds?

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.

\

$$\begin{array}{|c|c|c|} \\hline \\text{age} & \\text{mean} & \\text{standard deviation} \\\\ \\hline \\text{7 years} & 49 \\text{ inches} & 2 \\text{ inches} \\\\ \\hline \\text{12 years} & 58 \\text{ inches} & 2.3 \\text{ inches} \\\\ \\hline \\end{array}$$

Explanation:

Calculate Jose's distance from the mean

Using the Distance from Mean knowledge point

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Calculate Jamal's distance from the mean

Using the Distance from Mean knowledge point

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Calculate standard deviations from the mean for Jose

Using the Z-Score Formula knowledge point

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Calculate standard deviations from the mean for Jamal

Using the Z-Score Formula knowledge point

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Answer:

Question 1

How many standard deviations is Jose's height from the mean height for 7-year-olds? <blank>1</blank>

Question 2

How many standard deviations is Jamal's height from the mean height for 12-year-olds? <blank>-1</blank>