Uniform Distribution

A discount brokerage firm states that the time between a customer order for a trade and the execution of the order is uniformly distributed between three minutes and fifteen minutes. If a customer orders a trade at 11:54 A.M., what is the probability that the order is executed after noon?

A) 0.500. B) 0.250. C) 0.750. My answer would be 0.5. QBank however says 0.75.

for it to be executed after noon, the transaction must take longer than 6 minutes.

Since order are executed between 3 to 15 minutes uniformly distributed, the probability that the order would take longer than 6 minutes to execute

= 1 - P(t<=6)

= 1 - (6-3)/(15-3)

= 0.75


The wording in the question makes it unclear whether 3 and 15 minutes timelapses are to include. When someone says that the order can be executed between 3 minutes and 15 minutes, I would assume it means 3<= t <=15. Luckily the questions are multiple-choice! Edit: It looks the question is more about continuous uniform distribution, and in that case p(t=3)=0 and p(t=15)=0, so then the question is pretty straightforward.

Yes: it’s clearly a continuous, uniform distribution.