Respuesta :
Answer:
0.0907 = 9.07% probability that the demand will exceed 240 cfs during the early afternoon on a randomly selected day.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Exponential distribution with mean 100 cfs (cubic feet per second):
This means that [tex]m = 100, \mu = \frac{1}{100} = 0.01[/tex]
(a) Find the probability that the demand will exceed 240 cfs during the early afternoon on a randomly selected day.
[tex]P(X > 240) = e^{-240*0.01} = 0.0907[/tex]
0.0907 = 9.07% probability that the demand will exceed 240 cfs during the early afternoon on a randomly selected day.
