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?\
\\( \circ -2 \\)\
\\( \circ -1 \\)\
\\( \circ 1 \\)\
\\( \circ 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 dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $x = 64$ (the life span of the appliance), $\mu=48$ (the mean life span), and $\sigma = 8$ (the standard deviation).

Step3: Substitute values into formula

Substitute $x = 64$, $\mu = 48$, and $\sigma=8$ into the z - score formula: $z=\frac{64 - 48}{8}$.
First, calculate the numerator: $64-48 = 16$.
Then, divide by the standard deviation: $\frac{16}{8}=2$.

Answer:

2 (corresponding to the option with value 2)