Math 118 (statistics)

Question

Suppose that water usages in American showers are normally distributed, with an average shower using 15.7 gallons, and a standard deviation of 3.2 gallons. Estimate the percentage of showers that used

(a) % of showers use between 9.3 and 22.1 gallons.

(b) % of showers use more than 18.9 gallons.

(c) % of showers use less than 9.3 gallons.

(d) According to the 2 Standard Deviation Rule, data values that are more than 2 standard deviations away from the mean of the distribution are considered to be "unusually high" or "unusually low." According to this rule, it would be unusual for an American shower to last more than gallons.

Answer 1

Hi Sara, you may wish to approach this problem in two steps:

1. Determine the number of gallons at one and two standard deviations above and below the average. You'll basically create a list of five numbers (high to low): Average plus 2 SD, Average plus 1 SD, Average, Average minus 1 SD, Average minus 2 SD.
2. Remember that 68% of values are expected to fall within the range of one standard deviation, and 95% of values are expected to fall within the range of two standard deviations.

The numbers in questions a, b, and c reflect the high and/or low ends of a standard-deviation range of the shower usage. So, when you compare each number against your list, you'll see which standard deviation and percentage fits. For question d, just find the top end of the range for two standard deviations.

Hope that helps!

Bill