Question

The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27, 2003. 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?

Answer 1

The probability of a day requiring more water than is stored in city reservoirs is 0.0013 or 0.13%. It is impossible to have a reservoir capacity that guarantees the demand will never be exceeded.

Step-by-step explanation:

To find the probability that a day requires more water than is stored in city reservoirs, we need to calculate the z-score for the demand on June 27, 2003. The z-score formula is z = (x - mu) / sigma, where x is the demand, mu is the mean, and sigma is the standard deviation.

z = (442 - 310) / 45 = 3

Using a standard normal distribution table, we can find that the probability of a z-score greater than 3 is approximately 0.0013. So, the probability that a day requires more water than is stored in city reservoirs is 0.0013 or 0.13%.

To find the reservoir capacity needed so that the probability of being exceeded is 1, we need to find the z-score that corresponds to a probability of 1. Using the standard normal distribution table, we see that there is no z-score for a probability of 1. This means that it is impossible to have a reservoir capacity that guarantees the demand will never be exceeded.