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

Explanation:

Step1: Recall z - score formula

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

Step2: Rearrange the formula for $x$

Starting from $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x-\mu$. Then add $\mu$ to both sides to get $x=\mu + z\sigma$.

Step3: Substitute given values

We are given that $\mu = 48$, $z=-3$, and $\sigma = 8$. Substitute these values into the formula $x=\mu+z\sigma$: $x = 48+(-3)\times8$.

Step4: Calculate the value of $x$

First, calculate $(-3)\times8=-24$. Then $x = 48-24=24$.

Answer:

24 months