Question

ag the z-score to the correct vox
an score of 100 and the standard deviation of 10, match each students score to its correct z-score.
student a: 110 →
student b: 90 →
student c: 100 →
1.0 -1.0 0.0

Explanation:

Step1: Recall z-score formula

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $\mu = 100$, $\sigma = 10$.

Step2: Calculate z-score for Student A

Substitute $x=110$, $\mu=100$, $\sigma=10$ into the formula:
$z = \frac{110 - 100}{10} = \frac{10}{10} = 1.0$

Step3: Calculate z-score for Student B

Substitute $x=90$, $\mu=100$, $\sigma=10$ into the formula:
$z = \frac{90 - 100}{10} = \frac{-10}{10} = -1.0$

Step4: Calculate z-score for Student C

Substitute $x=100$, $\mu=100$, $\sigma=10$ into the formula:
$z = \frac{100 - 100}{10} = \frac{0}{10} = 0.0$

Answer:

Student A: 110 $
ightarrow$ 1.0
Student B: 90 $
ightarrow$ -1.0
Student C: 100 $
ightarrow$ 0.0