Respuesta :
Answer:
74.64% probability that the distance is at most 100 m
93.57% probability that the distance is at most 200 m
18.93% probability that the distance is between 100 and 200m.
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]
In this problem, we have that:
[tex]\mu = 0.01372[/tex]
What is the probability that the distance is at most 100 m?
[tex]P(X \leq 100) = 1 - e^{-0.01372*100} = 0.7464[/tex]
74.64% probability that the distance is at most 100 m
At most 200 m?
[tex]P(X \leq 200) = 1 - e^{-0.01372*200} = 0.9357[/tex]
93.57% probability that the distance is at most 200 m
Between 100 and 200 m?
0.9357 - 0.7464 = 0.1893
18.93% probability that the distance is between 100 and 200m.
