Question

Suppose the distribution of personal daily water usage in California is normally distributed with a mean of 18 gallons and a variance of 36 gallons.

a. The percentage of the population which uses more than 18 gallons is closest to which of the following?

b. Because of a perpetual water shortage in California, the governor wants to give a tax rebate to the 20 percent of the population who use the least amount of water. The maximum water limit for a person to qualify for a tax rebate should be set closest to which of the following?

Answer 1

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 18 gallons

Variance = 36 gallons^2

Standard deviation = = 6 gallons

a. Since 18 is the mean, percentage of the population which uses more than 18 gallons is closest to 50%

b. Let W be the maximum water limit for a person to qualify for a tax rebate.

P(X < W) = 0.20

P(Z < (W - 18)/6) = 0.20

Take the value of Z corresponding to 0.20 from standard normal distribution table.

(W - 18)/6 = -0.84

W = 12.96 gallons