# Finding a Percentile for a Uniform Distribution

This is a video on percentiles and the uniform

distribution. The question states: The amount of time one has to wait for a

museum tour is uniformly distributed from 0 to 45 minutes. Find the 80th percentile. I will start

out by putting this in a diagram. Since we have a uniform distribution, we get a

rectangle. We are going from 0 to 45 on the x-axis and the height of this

rectangle must be 1/45, so that the area is the base times the height. We want to find the 80th

percentile. We want to find the number k such that 80% of the data falls below that number k. In

other words, the area of this subrectangle, everything to the left of k must be 0.80 or 80%.

Now I compute the area in two different ways. which is the base which is k, times the height

which is 1/45.

Secondly, we know from before the area is supposed to be 0.80. Now I can

solve this by multiplying left and right by 45 I get k=(45)(0.80) and I arrived at 36 when I

calculated this. Now I am ready to state my conclusion. I can conclude that the 80th

percentile for the waiting time for the museum

tour is 36 minutes. I am done with the problem.

## 7 Replies to “Finding a Percentile for a Uniform Distribution”

You have no idea how much this video helped me! Thank you!

Man this is a great video but what the hell is happening when you get to percentiles!!! "The base which is K" so K is what?? This needs to be explained in simpler terms.

K is just the number of minutes waited that corresponds to the 80th percentile. The x-axis is minutes, so the K is placed on the x-axis. Notice that the "box" of the uniform distribution has base that goes from 0 minutes to 45 minutes. K is some number of minutes between 0 and 45. The point of the video is to find this K number of minutes. I hope this doesn't just confuse you more.

Thanks, you're video actually helped alot. It was the way the jackash that wrote our textbook worded the question that was screwing it all up. We didn't start at 0. we started at 25. So a=25 and b=45. So basically I just had to do the math you showed but then add it to 25. So to find the 90th percentile was 1/20 (so 20) 20*.90=18 What was screwing it all up was having to add 18 to a(25) to get 43. This video is awesome though thanks!

uhh isnt it easier to just do 45/100 = .45 (1%) and then multiply that by 80….

Please never start a video by saying "This is a video … "

You’re a fucking idiot the lower bound isn’t always going to be 0