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

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=(X-\mu)/(\sigma)`

`\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5*1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches`

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