Question

The mayor of the city of Detroit was informed that household water usage was a normally distributed random variable with a mean of 25 gallons and a standard deviation of 4 gallons per day.

a) Find the probability that a randomly chosen household uses fewer than 21 gallons per

day.

b) The mayor advertised on a local TV channel for about three weeks his intention to give a

tax rebate to the 20% lowest water users. If the advertisement lowered the mean usage of 25 gallons to 21 gallons, what should the gallons per day cutoff be?

Answer 1

Solution :

mean = 25

standard deviation = 4

a)

P(X < 21) = P ( Z < -1.00) = 0.1587

Answer: 0.1587

b)

mean = 21

standard deviation = 4

for below 20% z = -0.84

cutoff = -0.84*4+21 = 17.64

Answer: 17.64