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