a citys annual rainfall totals are normally distributed, and the probability that the city gets more than…

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 know that $P(z\geq1.5) = 0.0668$, and we are given $x = 43.2$ inches and $\sigma=1.8$ inches. We want to find $\mu$.

Step2: Rearrange the z - score formula for $\mu$

Starting from $z=\frac{x - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=x-\mu$. Then, we can solve for $\mu$: $\mu=x - z\sigma$.

Step3: Substitute the known values

We know that $z = 1.5$, $x = 43.2$ inches, and $\sigma = 1.8$ inches. Substituting these values into the formula $\mu=x - z\sigma$, we get $\mu=43.2-1.5\times1.8$.

Step4: Calculate the value of $\mu$

First, calculate $1.5\times1.8 = 2.7$. Then, $\mu=43.2 - 2.7=40.5$ inches.

Answer:

40.5 inches