the set of life spans of an appliance is normally distributed with a mean μ = 48 months and a standard…

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

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

Answer

Answer:

D. 2

Explanation:

Step1: Recall z - score formula

The z - score formula 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 given values

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

Step3: Substitute values into formula

$z=\frac{64 - 48}{8}$.

Step4: Calculate the numerator

$64-48 = 16$. So, $z=\frac{16}{8}$.

Step5: Calculate the z - score

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