Question

a standardized exams scores are normally distributed. in a recent year, the mean test score was 20.8 and the standard deviation was 5.7. the test scores of four students selected at random are 14, 21, 9, and 37. find the z - scores that correspond to each value and determine whether any of the values are unusual.
the z - score for 14 is
(round to two decimal places as needed.)

Explanation:

Step1: Recall z - score formula

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $\mu = 20.8$ and $\sigma=5.7$.

Step2: Calculate z - score for $x = 14$

Substitute $x = 14$, $\mu = 20.8$, and $\sigma = 5.7$ into the formula: $z=\frac{14 - 20.8}{5.7}=\frac{-6.8}{5.7}\approx - 1.19$.

Answer:

$-1.19$