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

Answer:

B. 24 months

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. We want to find $x$, and we know that $z = - 3$, $\mu=48$, and $\sigma = 8$.

Step2: Rearrange the formula for $x$

Starting with $z=\frac{x - \mu}{\sigma}$, 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 the given values

Substitute $\mu = 48$, $z=-3$, and $\sigma = 8$ into the formula $x=\mu+z\sigma$. So $x=48+(-3)\times8$.

Step4: Calculate the value of $x$

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