Respuesta :
Answer:
a) 0.25
b) 52.76% probability that a person waits for less than 3 minutes
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \lambda e^{-\lambda x}[/tex]
In which [tex]\lambda = \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 = 4[/tex]
a. Find the value of λ.
[tex]\lambda = \frac{1}{m} = \frac{1}{4} = 0.25[/tex]
b. What is the probability that a person waits for less than 3 minutes?
[tex]P(X \leq 3) = 1 - e^{-0.25*3} = 0.5276[/tex]
52.76% probability that a person waits for less than 3 minutes
