Question

The average annual rainfall in City A is 20 inches, with a standard deviation of 3 inches. The annual rainfall in City B is 45 inches, with a standard deviation of 12 inches. In a given year, City A received 25 inches, while City B received 55 inches. Assuming both rainfall distributions are approximately normal, which city had the wettest year relative to its average distribution?

a.City A

b.City B

c.The cities had equally wet years

d.Cannot tell from the information given

Answer 1

For City A, Z-score = (X - )/

                              = (25 - 20)/3

                              = 1.67

For City B, Z-score = (X - )/

                              = (55 - 45)/12

                              = 0.83

Since the z-score for City A is greater than the z-score for City B, so City A had the wettest year relative to its average distribution.

Option - A) City A