Question 730917
New York receives an average of 35.4 inches of rain each year with a standard deviation of 4.2 inches. Assume a normal model applies.
What is the probability that a student (in this area) will see an AVERAGE of less than 30 inches of rain in their four years? 
I know the probability of getting less than 30 in one year is 9.85%. I am just unsure about the average for the combination of the 4 years. 
z(30) = (30 - 35.4) / 4.2 = 1.286 (z-score) -> 0.0985
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In 4 years you have a sample of size n = 4
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The Central Limit Theorem says the standard deviation then 4.2/sqrt(4) = 2.1
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z(30) = (30-35.4)/2.1 = -2.5714
P(x-bar < 30) = P(z < -2.5741) = normalcdf(-100,-2.5741) = 0.005 or 0.5%
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Cheers,
Stan H.
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