the times it takes runners to complete a certain marathon are normally distributed with a mean of 4.6 hours…

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 want to find $x$, and we know that $z=- 1.2$, $\mu = 4.6$, and $\sigma=1.1$.

Step2: Rearrange the formula to solve 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 known values

Substitute $\mu = 4.6$, $z=-1.2$, and $\sigma = 1.1$ into the formula $x=\mu+z\sigma$. So $x=4.6+( - 1.2)\times1.1$.

Step4: Calculate the value of $x$

First, calculate $( - 1.2)\times1.1=-1.32$. Then $x=4.6-1.32 = 3.28$.

Answer:

$3.28$