uniform distribution

#1
A manager of a store reports that the time of a customer on the second floor must wait for the elevator has a uniform distribution ranging from 2 to 6 minutes. If it takes the elevator 15 seconds to go from floor to floor, find the probability that a hurried customer can reach the first floor in 2.5 minutes after pushing the elevator button on the second floor.

for uniform dist. f(y) = 1/(6-2)= 1/4. So I tried integrating that from 0 to 2.5, but it didn't work. I think I'm missing something, but I can't put my finger on it. Please help!
 
#2
Hi megs915,

The customer needs to wait for the elevator, then it would take 15 sec to get to 1st floor.

2.5 min=150sec, so he needs to wait for 150-15=135sec
The uniform distribution ranges from 120sec to 360 sec. Thus the probability is :

(135-120)/(600-120)
 

JohnM

TS Contributor
#4
quark said:
Hi megs915,

The customer needs to wait for the elevator, then it would take 15 sec to get to 1st floor.

2.5 min=150sec, so he needs to wait for 150-15=135sec
The uniform distribution ranges from 120sec to 360 sec. Thus the probability is :

(135-120)/(600-120)
Maybe I'm just missing something, but if it takes the elevator 15 seconds to go from floor to floor, it will take 15 seconds for it to go from the 2nd floor to the 1st floor - wouldn't this get added as a "constant" to the uniform distribution?

If the uniform distribution of waiting time ranges from 2 to 6 minutes, we add 15 seconds to it, to get 2.25 to 6.25, which includes waiting time plus travel time (for 1 floor in this case).

Then the probability of getting from the 2nd floor to the 1st floor in 2.5 minutes (or less) would be:

(2.5 - 2.25) / (6.25 - 2.25) = 0.25/4 = 1/16 = 0.0625
 
#5
John, thanks for pointing it out.

I had a typo in the solution. since 6 min =360 sec, it should be

(135-120)/(360-120) = 15/240 = 0.0625