Question

The average precipitation for the first 7 months of the year is 19.32 inches with a standard deviation of 2.4 inches. Assume that the average precipitation is normally distributed. What is the probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months?

Answer 1

Let $X=$ precipitation: $X\sim N(\mu, \sigma^2).$

Given $\mu=19.32\ in, \sigma=2.4\ in.$

$$P(X>18)=P(Z>\dfrac{18-19.32}{2.4})$$

$$=P(Z>-0.55)\approx0.70884$$