Question

Metro buses are scheduled to arrive at each stop every 30 minutes. If the time a person waits at a bus stop is uniformly distributed and the maximum possible wait time for a bus is 30 minutes, what is the probability that you will wait more than 25 minutes for a bus

Answer 1

The probability is
`P(X > 25 ) = 1.667`

Explanation:

From the question we are told that

The maximum wait is
`b = 30 \ minutes`

The minimum wait would be
`a = 0\ minutes`

Generally the probability that you will wait more than 25 minutes for a bus is mathematically represented as

`P(X > 25 )`

Now given that the time a person waits is uniformly distributed and that the maximum is 30 then we can evaluate the above probability as

`P(X > 25 ) = P(25 < X < 30 ) = (30 - 25)/(30 - 0)`

`P(X > 25 ) = 1.667`