"The records of the National Weather Service indicate that, on the average, the city of San Jose receives 14.03 inches of rain each year, with a standard deviation of 5.19 inches." In what percentage of years would you expect there to be less than 12 inches of rain?
A) -.39%
B) 15.17%
C) 34.83%
D) 65.17%

Question

Quizplus · Accepted Answer

To find the percentage of years with less than 12 inches of rain, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (12 inches), μ is the mean (14.03 inches), and σ is the standard deviation (5.19 inches). Plugging in the values: Z = (12 - 14.03) / 5.19 = -2.03 / 5.19 ≈ -0.39. Looking up -0.39 on a standard normal distribution table or using a calculator gives us an area to the left of approximately 34.83%, which represents the percentage of years with less than 12 inches of rain.

"The Records of the National Weather Service Indicate That, on the Average