"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." How many inches of rain must fall for a year to be in the top 10%?
A) 6.64
B) 10.38
C) 15.33
D) 20.67

Question

"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." How many inches of rain must fall for a year to be in the top 10%?
A) 6.64 
B) 10.38
C) 15.33
D) 20.67

Quizplus · Accepted Answer

To find the number of inches of rain that must fall for a year to be in the top 10%, we use the z-score formula associated with the top 10% of a normal distribution. The z-score for the top 10% is approximately 1.28. We then apply the formula: X = μ + zσ, where μ is the mean (14.03 inches), σ is the standard deviation (5.19 inches), and z is the z-score (1.28). Plugging in the values, we get X = 14.03 + (1.28)(5.19) ≈ 20.67 inches.

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