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Statistics from a college's climate center indicate that the city the college is in receives an average of 35.9" of rain each year, with a standard deviation of 4.3". Assume that a Normal model applies. Complete parts a through d below.

a) During what percentage of years does this city get more than 42" of rain?

The percentage of years with more than 42" of rain is __%. (Round to two decimal places as needed.)

Answer :

The required percentage of years with more than 42" of rain is 7.64% (option c).

Statistics from a college's climate center indicate that the city the college is in gets an average of 35.9" of rain each year, with a standard deviation of 4.3".

Let X be the amount of rain in the city each year and assume X follows Normal distribution. Here the mean is μ = 35.9 and the standard deviation is σ = 4.3. We need to find the percentage of years with more than 42" of rain.The probability that X is greater than 42 isP(X > 42)

First, we need to standardize 42 into a z-score using the formula

z = (x - μ)/σ

z = (42 - 35.9)/4.3

z = 1.43

Now, we need to find P(Z > 1.43) using a Standard Normal Table.P(Z > 1.43) = 0.0764Therefore, the percentage of years with more than 42" of rain is 0.0764 x 100% = 7.64%

Hence, option (C) is the correct answer.

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