Respuesta :
Using the Poisson distribution, it is found that P(X = 1) = 0.3599.
We have only the mean, hence, the Poisson distribution is used to solve this question.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
- x is the number of successes
- e = 2.71828 is the Euler number
- [tex]\mu[/tex] is the mean in the given interval.
In this problem, the mean is of 0.0864 failures per 100 miles per day, that is, 0.0864 failures per 161 km, hence, per 1500 km:
[tex]\mu = \frac{1500}{161} \times 0.0864 = 0.8053[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 1) = \frac{e^{-0.8053}(0.8053)^{1}}{(1)!} = 0.3599[/tex]
To learn more about the Poisson distribution, you can take a look at https://brainly.com/question/13971530
