Question

The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/15 where x goes between 4 and 19 minutes. Find the probability that the time will be at most 15 minutes.

Answer 1

73.33% probability that the time will be at most 15 minutes.

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

`P(X \leq x) = (x - a)/(b-a)`

Uniform distribution between 4 and 19 minutes.

This means that
`a = 4, b = 19`

Find the probability that the time will be at most 15 minutes.

`P(X \leq x) = (x - a)/(b-a)`

`P(X \leq 15) = (15 - 4)/(19 - 4) = 0.7333`

73.33% probability that the time will be at most 15 minutes.