Question

a standardized exams scores are normally distributed. in a recent year, the mean test score was 20 and the standard deviation was 5.7. the test scores of four students selected at random are 12, 21, 8, and 36. find the z - scores that correspond to each value and determine whether any of the values are unusual. the z - score for 12 is - 1.53. (round to two decimal places as needed.) the z - score for 21 is . (round to two decimal places as needed.)

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 20$ and $\sigma=5.7$.

Step2: Calculate the z - score for $x = 21$

Substitute $x = 21$, $\mu = 20$, and $\sigma = 5.7$ into the formula: $z=\frac{21 - 20}{5.7}=\frac{1}{5.7}\approx0.18$.

Answer:

0.18