The operator of a pumping station has observed that demand

Chapter 4, Problem 91E

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QUESTION:

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

a Find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day.

b What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only .01?

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QUESTION:

The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second).

a Find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day.

b What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only .01?

ANSWER:

Step 1 of 3

Given

The population of that demand for water during early afternoon hours has an approximately exponential distribution

Population mean \(\beta\) = 100 cfs

a. The demand for water greater than random variable, Y = 200

b. The water pumping capacity, random variable, Y = C

The probability of demand for water to exceed capacity C,  P(Y > C) = 0.01

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