Question

Suppose Busses arrive at a bus stop uniformly in 8 minute windows with a uniform probability. What is the probability you would have to wait more than 5.5 minutes for the next bus?

Answer 1

The probability of waiting more than 5.5 minutes for the next bus, given a uniform 8-minute arrival window, is 31.25%.

Step-by-step explanation:

The probability that you would have to wait more than 5.5 minutes for the next bus can be calculated using the properties of a uniform distribution. Since buses arrive uniformly in 8-minute windows, the waiting time from 0 to 8 minutes is equally likely at any point.

Here is the step-by-step explanation for calculating the probability:

1. The total duration of the window is 8 minutes.
2. You want to find the probability of waiting more than 5.5 minutes, so we calculate the length of the interval from 5.5 to 8 minutes, which is 2.5 minutes.
3. To find the probability, divide the interval length by the total window length: Probability = 2.5 / 8.
4. Complete the calculation: Probability = 0.3125 or 31.25%.

Therefore, the probability that you will wait more than 5.5 minutes for the next bus is 31.25%.