Question

In Santa Clara University, students arrive at Benson food court with an arrival rate of 4 students per minute. The probability that the time between two successive student arrivals at Benson is greater than 2 minutes is:

Answer 1

The probability that the time between two successive student arrivals at Benson is greater than 2 minutes is 0.000335.

Step-by-step 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:

`F(x)=1-e^(-Lx)`

where L = Arrival rate of students (per minute) = 4

Hence,

`F(x)=1-e^(-4x)`

We require the probability that the time between two successive arrivals is greater than 2 minutes. Therefore,

`P(X>2)=1-F(2)`

`P(X>2)=1-(1-e^(-4(2)))`

`P(X>2)=e^(-8)`

`P(X>2)=0.000335`