The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27, 2003 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons.

(a) What is the probability that a day requires more water than is stored in city reservoirs?

(b) What reservoir capacity is needed so that the probability that it is exceeded is 1%?

(c) What amount of water use is exceeded with 95% proba- bility?

(d) Water is provided to approximately 1.4 million people. What is the mean daily consumption per person at which the probability that the demand exceeds the current reser- voir capacity is 1%? Assume that the standard deviation of demand remains the same.