Question

the set of life spans of an appliance is normally distributed with a mean $mu = 48$ months and a standard deviation $sigma = 8$ months. what is the z - score of an appliance that stopped working at 64 months?
-2
-1
1
2

Explanation:

Step1: Recall z - score formula

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

Step2: Identify values

We are given that $\mu = 48$, $\sigma=8$, and $x = 64$.

Step3: Substitute values into formula

$z=\frac{64 - 48}{8}=\frac{16}{8}=2$

Answer:

D. 2