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 [tex]\sigma[/tex]=1.8 inches
We know that [tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5\times1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches[/tex]
Hence, the city’s mean annual rainfall is 40.5 inches.
