Sure! Let's work through the question step by step:
### Given Data:
- Jordan's height: 53 inches
- Jake's height: 44 inches
- Jacob's height: 49 inches
- Standard deviation ([tex]\(\sigma\)[/tex]): 5 inches
- Mean height ([tex]\(\mu\)[/tex]): 50 inches
### Formula for z-score:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
where [tex]\( x \)[/tex] is the height of the student, [tex]\( \mu \)[/tex] is the mean height, and [tex]\( \sigma \)[/tex] is the standard deviation.
### 1. Calculating Jordan's z-score:
[tex]\[ z_{\text{Jordan}} = \frac{53 - 50}{5} = \frac{3}{5} = 0.6 \][/tex]
Jordan's z-score is 0.6.
### 2. Calculating Jake's z-score:
[tex]\[ z_{\text{Jake}} = \frac{44 - 50}{5} = \frac{-6}{5} = -1.2 \][/tex]
Jake's z-score is -1.2.
### 3. Calculating Jacob's z-score:
[tex]\[ z_{\text{Jacob}} = \frac{49 - 50}{5} = \frac{-1}{5} = -0.2 \][/tex]
Jacob's z-score is -0.2.
### 4. Finding the height of a student whose z-score is 3:
We can rearrange the z-score formula to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \mu + z \cdot \sigma \][/tex]
If the z-score is 3, then:
[tex]\[ x = 50 + 3 \cdot 5 = 50 + 15 = 65 \][/tex]
So, the height of a student whose z-score is 3 is 65 inches.
### Summary of Answers:
1. Jordan's z-score: 0.6
2. Jake's z-score: -1.2
3. Jacob's z-score: -0.2
4. Height of a student whose z-score is 3: 65 inches
