standard deviatin the summer is normally distributed with a mean 310 million gal

Question

standard deviatin the summer is normally distributed with a mean 310 million gallons per day and a nearly 350 million gallons (a) Wh for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June dS million gallons per day. City reservoirs have a combined storage capacity of b) wha s he probability that a day requires more water than is stored in city reservoirs? (c) What a r capacity is needed so that so that the probability that it is exceeded is 1%? (d) W ater 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 reservoir capacity is 1%? Assume the standard deviation of demand remains the same.

Explanation / Answer

a) P(X > 350)
=P(Z >(350 - 310)/45)
= P (Z>0.89)=0.1867

b) P(Z > z*) = 0.01
z* = 2.327
X = 310 + 2.327 * 45 = 414.715

c)
310 - 1.96 * 45 =221.8
310 +1.96 *45 = 398.2

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