Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed,
with a mean of 35.5 inches and a standard deviation of 2.5 inches.
(a) About 2.5% of the years, the annual rainfall will exceed how many inches?
(Round your answer to one decimal place.)
(b) About what percent of the years will it rain more than 38 inches in Ferndale?
(Round your answer to two decimal places.)
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(a) Go to website https://onlinestatbook.com/2/calculators/inverse_normal_dist.html
and use free of charge online calculator there (Inverse Normal Distribution).
It allows calculate the scores given the area (percentage of the area) under the normal curve.
Input the mean 35.5 and SD 2.5 in appropriate windows.
Input 0.025 (which represents 2.5%) in the window "Area".
Press the button "Recalculate" and get the answer 40.40 in the window "Above".
ANSWER. About 2.5% of the years, the annual rainfall will exceed 40.4 inches in Ferndale.
(b) Go to website https://onlinestatbook.com/2/calculators/normal_dist.html
and use free of charge online calculator there (Normal Distribution).
It allows calculate the area (percentage of the area) under the normal curve for given scores.
Input the mean 35.5 and SD 2.5 in appropriate windows.
Input 38 (which represents 38 inches) in the window "Above".
Press the button "Recalculate" and get the answer 0.1587 in the window "Above".
ANSWER. About 15.87% of the years, the annual rainfall will exceed 38 inches in Ferndale.