Question

some descriptive statistics for a set of test scores are shown above. for this test, a certain student has a standardized score of z = -1.2. what score did this student receive on the test? variable score n 50 minimum 628.9 mean 1045.7 median 1024.7 trmean 1041.9 stddev 221.9 se mean 31.4 maximum 1577.1 q1 877.7 q3 1219.5 a 266.28 b 779.42 c 1008.02 d 1083.38 e 1311.98

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 need to solve for $x$. Rearranging the formula gives $x=z\sigma+\mu$.

Step2: Identify values from the table

From the table, $\mu = 1045.7$, $\sigma=221.9$, and $z = - 1.2$.

Step3: Substitute values into the formula

$x=(-1.2)\times221.9 + 1045.7$.
First, calculate $(-1.2)\times221.9=-266.28$.
Then, $x=-266.28 + 1045.7$.
$x = 779.42$.

Answer:

B. 779.42