A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43 point 2 inches of rain in a year is given by cap p times open paren z is greater than or equal to 1 point 5 close paren is equal to 0 point 0 6 6 8 If the standard deviation of the city’s yearly rainfall totals is 1 point 8 inches, what is the city’s mean annual rainfall?
The rainfall amount of 43.2 inches is 1.5 standard deviations above the mean, since the given upper-tail probability corresponds to z = 1.5. Thus, 43.2 = mean + 1.5(1.8) = mean + 2.7, so the mean is 43.2 − 2.7 = 40.5 inches. The correct choice is 40.5 inches.
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