) 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 120 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) b. What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.09? (Round your answer to two decimal places.)

a) 0.3012 = 30.12% probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

b) 240.79 cfs.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

The probability of finding a value higher than x is:

In this problem, we have that:

a. Find the probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

This is

0.3012 = 30.12% probability that the demand will exceed 120 cfs during the early afternoon on a randomly selected day.

b. What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.09?

We want x for which

So

So 240.79 cfs.

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