Question

the waiting times between a subway departure and the arrival of a passengers are uniformly distributed between 0 and 7 minutes find the probability that a randomly selected passenger has a waiting time greater than 3.25 minutes

Answer 1

We have the variable "waiting time" as a random variable uniformly distributed between 0 and 7 minutes.

We have to find the probability that the waiting time is greater than 3.25 minutes.

We can see the probability as the "green" area in the

We can calculate this probabilty as:

$P(t>3.25)=\frac{t_{\max}-3.25}{t_{\max}-t_{\min}}=\frac{7-3.25}{7-0}=\frac{3.75}{7}\approx0.536$

NOTE: we can also have calculated the area (1/7)*(7-3.25) with the same result.

Answer: the probability of a waiting time greater than 3.25 is P(t>3.25)=0.536 or 53.6%.