Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with a mean of 39.5 inches and a standard deviation of 3.5 inches. About 2.3% of the time, the annual rainfall will exceed how many inches?
A) 39.5 inches
B) 32.5 inches
C) 43 inches
D) 36 inches
E) 46.5 inches

Question

Quizplus · Accepted Answer

To find the rainfall amount exceeded about 2.3% of the time, we look for a value in the upper tail of the normal distribution. The Z-score corresponding to 2.3% in the upper tail is approximately 2 standard deviations above the mean (more precisely, it's closer to 2 but for simplicity, we approximate). Using the formula: Value = Mean + (Z * Standard Deviation), where Mean = 39.5 inches, Standard Deviation = 3.5 inches, and Z ≈ 2, we get: Value ≈ 39.5 + (2 * 3.5) = 39.5 + 7 = 46.5 inches.

Suppose That the Annual Rainfall in Ferndale, California, Is Known