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?$\bigcirc$ -2$\bigcirc$ -1$\bigcirc$ 1$\bigcirc$ 2

Explanation:

Step1: Recall z-score formula

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

Step2: Substitute given values

Substitute $x=64$, $\mu=48$, $\sigma=8$ into the formula:
$z = \frac{64 - 48}{8}$

Step3: Calculate numerator first

$64 - 48 = 16$

Step4: Compute final z-score

$z = \frac{16}{8} = 2$

Answer:

2