Respuesta :
Answer:
0.9179 = 91.79% probability that a randomly selected call time will be less than 25 seconds
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]
In this question:
[tex]m = 10, \mu = \frac{1}{10} = 0.1[/tex]
Find the probability that a randomly selected call time will be less than 25 seconds?
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
[tex]P(X \leq 25) = 1 - e^{-0.1*25} = 0.9179[/tex]
0.9179 = 91.79% probability that a randomly selected call time will be less than 25 seconds
