The daily water consumption of a city may be assumed to be a normal random variable ...

The daily water consumption of a city may be assumed to be a normal random variable, with a mean of 500,000 gal/day (gpd) and a standard deviation of 150,000 gpd.    The daily water supply is either 600,000 or 750,000 gpd, with probabilities of 0.7 and 0.3, respectively.

1) What is the probability of a water shortage in any given day? (Ans. 0.191)

2) What is the probability of a shortage during one week, assuming that demand and capacity are statistically independent on any given day? (Ans. 0.774)

3) If the occurrence of water shortages is modeled as a Poisson process, what is the probability of a shortage during any week? (Ans. 0.737)

4) If the city engineer wants the probability of shortage to be no more than 0.01 on any given day, what water supply is required? (Ans. 848,900 gpd)