00:01
So we have a uniform distribution, and we know that a density curve has the area underneath it of one.
00:06
So if the distance between the top and the bottom is 2 .5, then this height of this rectangle has to be 1 over 2 .5, and i'll just leave it as an improper fraction.
00:17
So we want to find the probability that the time will take more than two minutes.
00:23
So two minutes is going to be somewhere in here, and we want to find that time above.
00:29
So when we mark two on here, and that two would actually be closer down here, only two we need to find what this area is.
00:38
And so that area, 4 minus 2 is 2.
00:41
That's how long that rectangle is, times 1 over 2 .5, and 2 divided by 2 .5 gives us 0 .8.
00:51
So it has a probability of 0 .8 or 80%.
00:55
Now, what's the likelihood that it will last less than 3? minutes.
01:01
So we want to find the area of that green rectangle.
01:06
And so we know that the distance between 3 and 1 .5, that is 1 .5, and then times 1 over or divided by 2 .5.
01:18
And so that is 15 over 25, and 5 goes into the top three times, and 5 goes into the bottom three times.
01:28
So 3 -fifths or point six.
01:31
Now we want to find the 30th percentile.
01:35
And so we want to find the value that is 30 percent of the way through this list.
01:40
So if we know that the distance between those two, the high and the low is 2 .5, we want to go only 30 percent of the way through that list.
01:50
So 0 .3 times 2 .5 gives us 0 .75...