Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1,300 gallons, and the standard deviation is 200 gallons.
What is the approximate value of the 98th percentile?

A)1,700 gallons
B)1,100 gallons
C)1,500 gallons
D)1,900 gallons
E)1,300 gallons

Question

Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound shaped and approximately symmetric. The mean is 1,300 gallons, and the standard deviation is 200 gallons. ​
What is the approximate value of the 98th percentile?
​
A)1,700 gallons
B)1,100 gallons
C)1,500 gallons
D)1,900 gallons
E)1,300 gallons

Quizplus · Accepted Answer

Given the distribution is mound-shaped and approximately symmetric, we can apply the empirical rule. The 98th percentile falls well beyond two standard deviations above the mean. Two standard deviations (2*200 = 400 gallons) above the mean (1,300 gallons) is 1,700 gallons. However, the 98th percentile is even further out, typically around three standard deviations above the mean in a normal distribution. Since the closest option to this calculation is 1,700 gallons, it is the best approximation given the choices.

Suppose That the Distribution of Weekly Water Usage for Single-Family