00:01
Okay, so here we're told a few different things.
00:04
We're told that the sample mean of 277 18 -year -old males for their waist recumference was 86 .3 centimeters.
00:14
And we're told a bunch of other things for the population percentiles.
00:20
The ones that i really want to worry about, first i want to look at the 50th percentile because that's the median.
00:26
Okay, so the 50th percentile is, let's see, 81 .3.
00:36
Okay.
00:38
And so we are asked, is it plausible that the waste size distribution is at least approximately normal? okay.
00:47
And as you can see here, there's a pretty big difference between the mean and the median here.
00:54
Like five is a pretty big difference.
00:56
And so i would say that since the mean and the median are pretty different, then it doesn't look like it's going to be symmetrical.
01:11
And, or yeah, it doesn't look like it's going to be symmetrical.
01:14
Now, the other thing that we need to do is i want to look at the distance between the 25th to the 50th percentile and then also the distance from the 50th to the 75th percentile.
01:26
And in a normal distribution, we would expect those distances to be pretty similar.
01:32
So the distance from the 50th to the 75th is like 14, right? eighty -one to 95 is about 14.
01:41
And the distance between the 25th and the 50th percentile is from 75 to 81, which is about 6.
01:49
And that distance is very different as well.
01:52
So i'm going to say that it does not look like it can be approximately normal.
01:59
Okay.
02:01
If we're going to make a conjecture about the shape, okay, we need to think about, like when i look at the fifth to the tenth percentile, right, it's very squished together.
02:17
And then when i get to the 75th and the like 90th in the 95th and the 95th percentile, it gets like much more spread out, right? the distance between the fifth and tenth percentiles, for example, is like one centimeter, and the distance from the 90th to the 95th percentiles is like nine, right? so that tells me that i've got kind of this thing probably going on, which would be right skewed...