Respuesta :
Answer:
The probability that the next customer will arrive in 3 minutes or less is 0.45.
Step-by-step explanation:
Let N (t) be a Poisson process with arrival rate λ. If X is the time of the next arrival then,
[tex]P(X>t)=e^{-\lambda t}[/tex]
Given:
[tex]\lambda=\frac{12}{60}[/tex]
t = 3 minutes
Compute the probability that the next customer will arrive in 3 minutes or less as follows:
P (X ≤ 3) = 1 - P (X > 3)
[tex]=1-e^{-\frac{12}{60}\times3}\\=1-e^{-0.6}\\=1-0.55\\=0.45[/tex]
Thus, the probability that the next customer will arrive in 3 minutes or less is 0.45.
The probability that the next customer will arrive in 3 minutes or less is; 0.4512
This is a Poisson distribution problem with the formula;
P(X > t) = e^(-λt)
Where;
λ is arrival rate
t is arrival time
We are given;
λ = 12/60
t = 3 minutes
- We want to find the probability that the next customer will arrive in 3 minutes or less. This is expressed as;
P (X ≤ 3) = 1 - (P(X > 3))
Thus;
P (X ≤ 3) = 1 - e^((12/60) × 3)
P (X ≤ 3) = 1 - 0.5488
P (X ≤ 3) = 0.4512
Read more about Poisson distribution at; https://brainly.com/question/7879375
