Question

What is the pero probability that ramdomly selected year will have precipitation greater than 18 inches for the first 7 months?

Answer 1

Let $X$ be a random variable representing the precipitation for the first 7 months of a year. $X$ follows a normal distribution with mean $\mu=19.32$ and standard deviation $\sigma=2.44$. We need to find the probability,

$p(X\gt 18)=p((X-\mu)/\sigma\gt (18-\mu)/\sigma)=p(Z\gt (18-19.32)/2.44)=p(Z\gt -0.5409836)$

This probability can be written as,

$p(Z\gt -0.5409836)=1-p(Z\lt -0.5409836)=1-0.2946=0.7054$

Therefore, the  probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is 0.7054.