Respuesta :
Answer:
0.685 = 68.5% probability that X is less than 30 minutes
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]
If X has an average value of 26 minutes
This means that [tex]m = 26, \mu = \frac{1}{26}[/tex]
What is the probability that X is less than 30 minutes?
[tex]P(X \leq 30) = 1 - e^{-\frac{30}{26}} = 0.685[/tex]
0.685 = 68.5% probability that X is less than 30 minutes
