Question

the average height of students in courtneys class is 5.5 feet, with a standard deviation of 0.4 feet. courtney is 6.3 feet tall. calculate the z - score for courtneys height.
a 1.5
b 2.5
c 1.8
d 2.1

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 5.5$ (mean height), $\sigma=0.4$ (standard deviation), and $x = 6.3$ (Courtney's height).

Step3: Substitute values into formula

$z=\frac{6.3 - 5.5}{0.4}=\frac{0.8}{0.4}$

Step4: Calculate z - score

$\frac{0.8}{0.4}=2$

Answer:

None of the provided options (A. 1.5, B. 2.5, C. 1.8, D. 2.1) are correct. The correct z - score is 2.