00:01
We have a uniform distribution here.
00:04
Let's draw it out.
00:08
And it's between 4 and 26.
00:10
So we'll put 4 and 26.
00:12
So this is a distribution where the probability of x being below 4 is 0.
00:18
When it jumps up, stays constant, and drops back down, so the probability of being above 26 is also 0.
00:26
But the probability of having any point in between is the same.
00:30
So for part a, we want the probability that x is between, 8 and 12.
00:36
So we have a sliver here of 8 and 12 and we want to know what this area here is because that will show us the probability.
00:46
So the best way to go about working this out is to look at these rectangles and we want to know how big this rectangle is compared to the entire rectangle and area of a rectangle is length times height.
01:02
So we have length times height over length times height to give us a ratio of the areas.
01:10
But the height is the same, they're all the same height, so these just can't slant.
01:14
And what we're left with is the length of this rectangle divided by the length of the big rectangle.
01:20
That will tell us what proportion of the overall rectangle is taken up in this little sliver here.
01:27
And that's the key to solving a uniform distribution question.
01:31
So the length of the red interval is 12 minus it's 4.
01:38
The length of the blue interval is 26 minus 4.
01:43
And this will give us the answer.
01:48
So we have 4 divided by 22, which is 0 .1818.
02:00
Part b, we want the probability between 11 and 22.
02:07
So very similar, except now we just change these...