Finding a Probability for a Uniform Distribution

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”

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

  2. 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?

  3. 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.

  4. Thanks for your videos on Probability. They’re very helpful. Going to watch the one on Binomial Probabilities. Thanks again.

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