Answer to Question #129483 in Statistics and Probability for Jasleen Dhillon

Question

: Students arrive at restaurant at an average rate of 5 in 15 minutes.
14. (6 points) The probability that 3 students arrive in 15 minutes is

Answer 1

Since we have some number of events (students coming into restaurant) occurring in a fixed interval of time (15 min) that have constant mean rate (5 in 15 minutes). Also, students come independently. This mean that time of arriving of next student doesn't depend on arriving of the previous one. We know that in this case it is Poisson distribution.

$P(x=k) = \frac{\lambda^k e^{-\lambda}}{k!}$

where $\lambda=5$ is the mean.

The probability that 3 students arrive in 15 minutes is

$P(x=3)= \frac{5^3*e^{-5}}{3!} = 0.14$