Answer:
The probability that the time between two successive student arrivals at Benson is greater than 2 minutes is 0.000335.
Explanation:
The arrival rate of students is 4 students per minute.
The time between 2 successive arrivals is a random variable having exponential distribution.
The formula for exponential distribution is:
[tex]F(x)=1-e^{-Lx}[/tex]
where L = Arrival rate of students (per minute) = 4
Hence,
[tex]F(x)=1-e^{-4x}[/tex]
We require the probability that the time between two successive arrivals is greater than 2 minutes. Therefore,
[tex]P(X>2)=1-F(2)[/tex]
[tex]P(X>2)=1-(1-e^{-4(2)})[/tex]
[tex]P(X>2)=e^{-8}[/tex]
[tex]P(X>2)=0.000335[/tex]
