00:01
So we are told that there is a right skewed distribution.
00:03
So i'll just draw a right skew here.
00:05
It looks like that.
00:06
Long right tail.
00:07
Draw it a bit more extreme, really show it.
00:10
Its mean is 480 minutes.
00:13
Its standard deviation, 40 minutes.
00:15
Duration of journeys from tallahassee to miami.
00:19
And we aren't looking at individual journeys here.
00:22
We're looking at 36 journeys.
00:24
What are the quartiles for the distribution of the average durations? so what would the distribution of sample means for samples of 36 journeys look like? well, i'm going to refer to the central limit theorem, which states that as sample size increases, sample means become more and more normally distributed.
00:44
If n is at least 30, you can treat them as approximately normal, even though they're coming from this right skewed distribution.
00:51
So if i took every sample of 36 journeys, found the averages and plotted them out, i'd get something approximately normal.
00:59
The mean of the means is the same as the population mean.
01:03
The standard deviation of the sample means, or standard error, is sigma over root n.
01:09
So that's 40 over root 36.
01:11
So 40 over 6, or 20 over 3.
01:14
We want the quartiles.
01:20
So i'll mark those on here.
01:22
Q1, q3.
01:24
And why not q2, just for the fun of it.
01:28
Q1 is the point on a distribution where 25 % of the time you go below that, 75 % above.
01:35
The third quartile is 75 % below, 25 % above...