1. 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 random chosen household uses more than 23 gallons per day.

b) Find the probability that a randomly chosen household uses between 20 and 25 gallons per day.

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

d) If the mayor wants to give a tax rebate to the 20% lowest water users, what should the gallons per day cutoff be?

e)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?