Uniform Distribution

[Oscar]

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.

 

[mkipa1]

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

 

[Oscar]

Thanks!

 

[OlegLukia]

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.

 

[S2000magician]

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