Question

A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668. If the standard deviation of the city’s yearly rainfall totals is 1.8 inches, what is the city’s mean annual rainfall?

Answer 1

40.5 is the city's mean annual rainfall.

Answer 2

Answer: 40.5 inches

Step-by-step explanation:

Given: A city’s annual rainfall totals are normally distributed.

The probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668

Thus, X=43.2 inches

z=1.5

Standard deviation $\sigma$=1.8 inches

We know that $z=\frac{X-\mu}{\sigma}$

$\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5\times1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches$

Hence,  the city’s mean annual rainfall is 40.5 inches.