Question

Suppose that at a particular bus stop, Brown buses arrive
according to a **Poisson process with a constant rate of 3
per hour**. The travel time on the Brown bus to your class
is 7 minutes. (The Brown bus drops you off at your
class.). When you approach the bus stop, you see that
you have just missed a Blue bus. Class starts in 20 minutes and it
is exam day so you want to get to class as soon as possible. What
is the probability that the Brown bus will get you to class on
time? Answer to 3 decimal places.

Answer #1

**Answer:**

Given,

To determine the probability that the Brown bus will get you to class on time

= 3/60 * 13

= 0.05*13

= 0.65

= 0.65

Now consider the poisson distribution

P(X = k) = e^-*^k / k!

P(X >= 1) = 1 - P(X = 0)

= 1 - e^-

= 1 - e^-0.65

= 1 - 0.522045776

= 0.477954223

= 0.478

Hence the probability that the Brown bus will get you to class on time is 0.478

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