Question

finding a data value from a z - score
mr. jackson gave an exam worth 50 points.
the mean score on the exam was 38, and the standard deviation was 4.
mr. jackson also reported his students’ z - scores.
corey’s z - score was - 1.75. this means that corey scored
square points on the exam.

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. We rearrange it to solve for $x$: $x = z\sigma + \mu$.

Step2: Substitute given values

We know $z=-1.75$, $\mu=38$, $\sigma=4$. Substitute these into the formula:
$x = (-1.75)(4) + 38$

Step3: Calculate the product

Compute $(-1.75)(4)$ first:
$(-1.75)(4) = -7$

Step4: Compute the final score

Add the result to the mean:
$x = -7 + 38 = 31$

Answer:

31