# Finding a Probability for a Uniform Distribution

0:00:00.000,0:00:09.000 This is a video on the uniform distribution. The question states: The waiting time for 0:00:09.000,0:00:19.066 the train that leaves every 30 minutes is

uniformly distributed from 0 to 30 minutes. Find the 0:00:19.066,0:00:28.033 probability that a person arriving at a random time will wait between 10 and 15 minutes. 0:00:28.033,0:00:37.000 Let’s start out by drawing a diagram. We have a uniform distribution. We always know 0:00:37.000,0:00:47.033 when we have a uniform distribution we get

a rectangle. The f(x) curve is horizontal. 0:00:47.033,0:00:53.066 We are going from 0 to 30, in terms of the

wait times. For the area of the rectangle to 0:00:53.066,0:01:04.033 equal 1, the height must be 1/30, because

1/30 times 30 equals 1. We want to find the 0:01:04.033,0:01:12.000 probability that the wait time is between

10 and 15 minutes. So we want the part of the 0:01:12.000,0:01:21.033 rectangle between 10 and 15. We want to find out its area. In particular, the probability that 0:01:21.033,0:01:29.000 the wait time x is between 10 and 15 is the

area of the rectangle which is the length of 0:01:29.000,0:01:35.000 the base, and that we can calculate by taking

15 and subtracting 10. We see that 0:01:35.000,0:01:47.000 that base is of lenght 5. Times the height. The height is 1/30. Then 15 – 10=5. Divide by 30 0:01:47.000,0:01:55.033 to get 5/30. We can reduce and say the probability is 1/6. Now I can state my conclusion. 0:01:55.033,0:02:04.066 In conclusion, the probability that a person arriving at a random time will wait between 0:02:04.066 10 and 15 minutes is 1/6. I am done with the problem.

## 23 Replies to “Finding a Probability for a Uniform Distribution”

Great explanation! It was very easy to follow

Dude you're awesome

Thank you for the help, even if you did read it like a creeper.

Great video! Thanks a bunch!!

nice simple example π

you rock !!

Thanks for posting this; it helped me a lot with some homework! π

thanks for simple example Β

thank you !!

thank you, good example

i understand the gist of it, but where does the 1/30 come from. Does that just mean 1 out of 30 minutes?

thank you so much π i hope you're still active in this account. You have helped so much people inclucing me π

This was a life saver π

thanks! this helped me a lot.

I was wondering if you help me with uniform

distribution from one to 53 (spread of 52)

P(12 < x|x < 28)

If, for instance, I wanted to calculate the probability that three people would have to wait between 10 and 15 minutes, provided that they are totally independent of each other, would I literally just cube the answer here, or is there something else going on?

thank you so much, you explained it perfectly!

that voice

this is exactly what ive been looking for

Found your video to clarify a jumbled mess regarding uniform distributions, excellent explanation, and the graphical representation was a huge plus! I hope you make future how-to videos using technology (Ti-84, Casio Fx-CG50) for statistics/business statistics students.

Thanks for your videos on Probability. Theyβre very helpful. Going to watch the one on Binomial Probabilities. Thanks again.

how to find f(x) ? please help ..

Short and powerful!!!