To calculate the z-scores for Jordan, Jake, and Jacob, we will use the given formula for the z-score:
[tex]\[
z = \frac{x - \mu}{\sigma}
\][/tex]
where:
- [tex]\(x\)[/tex] is the individual height,
- [tex]\(\mu\)[/tex] is the mean height,
- [tex]\(\sigma\)[/tex] is the standard deviation.
Given:
- Mean height ([tex]\(\mu\)[/tex]) = 49 inches,
- Standard deviation ([tex]\(\sigma\)[/tex]) = 2 inches.
Let's calculate the z-scores step by step:
### 1. Jordan's z-score:
- Jordan's height ([tex]\(x\)[/tex]) = 53 inches.
[tex]\[
z = \frac{53 - 49}{2} = \frac{4}{2} = 2.0
\][/tex]
So, Jordan's z-score is [tex]\(2.0\)[/tex].
### 2. Jake's z-score:
- Jake's height ([tex]\(x\)[/tex]) = 44 inches.
[tex]\[
z = \frac{44 - 49}{2} = \frac{-5}{2} = -2.5
\][/tex]
So, Jake's z-score is [tex]\(-2.5\)[/tex].
### 3. Jacob's z-score:
- Jacob's height ([tex]\(x\)[/tex]) = 49 inches.
[tex]\[
z = \frac{49 - 49}{2} = \frac{0}{2} = 0.0
\][/tex]
So, Jacob's z-score is [tex]\(0.0\)[/tex].
### Summary:
- Jordan is 53 inches tall. What is his z-score? [tex]\(2.0\)[/tex]
- Jake is 44 inches tall. What is his z-score? [tex]\(-2.5\)[/tex]
- Jacob is 49 inches tall. What is his z-score? [tex]\(0.0\)[/tex]
