The average annual snowfall in City A is 20 inches, with a standard deviation of

Question

The average annual snowfall in City A is 20 inches, with a standard deviation of 8 inches. The average annual snowfall in City B is 100 inches, with a standard deviation of 25 inches. In a given year, City A received 28 inches, while City B received 120 inches. Assuming both snowfall distributions are approximately normal, which city had the snowiest winter that year relative to its average distribution?

A. City A

B. City B

C. The cities had equally severe winters.

D. Cannot tell from the information given.

Explanation / Answer

Z scores can be used to compare the snowfall of the two cities

Z = (X - mean)/standard deviation

For City A, Z score = (28-20)/8 = 1

For City B, Z score = (120-100)/25 = 0.8

Z score is higher for City A, so, City A had the snowiest winter that year relative to its average distribution

A. City A

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