00:01
All right, i'm going to try my best to explain this in simplest terms.
00:04
The scores on a hundred point exam are normally distributed with a mean of 80 and standard deviation of 6.
00:10
A student score places him in the 69th and 70th percentile, which of the following best represents his score.
00:18
So without getting too complicated, because this is normally distributed, this is not very good normally distributed graph, but it'll do.
00:30
I'm going to explain that in the middle is always your mean.
00:35
And the mean in this case is 80.
00:38
And then if we are one standard deviation away, we are jumping up to 86 because, again, the standard deviation is 6.
00:48
So 80 plus 6 is 86.
00:50
Okay.
00:52
And so if we were just to think about this, if we were thinking about the empirical rule, the empirical rule, let me change color, says that if we are one standard deviation away from the mean on each side, everything inside these red lines, between these red lines, add up to about 68%.
01:17
So if we were to cut that in half, that would be 34 % on this side, and that would be 34 % on this side.
01:25
Okay? so if we're thinking about it like that, the reason, why that's important is because the 80, right in the middle, the mean, that represents 50 % of the data, right? so that's like the 50th percentile.
01:43
So if we were to take the 50 % and add the 34%, that means at the next standard deviation, that's about 84 % of the data.
01:57
Or like it bumps you in the 84th percentiles, is what i'm trying to say.
02:02
So we need somewhere between the 50th percentile and 84th percentile, right? because that's where we're going to get the 69th and 70.
02:11
So i'm just having you think about, like, just thinking about it what that means.
02:15
So basically it's kind of like, yeah, we know our answer is going to be between 80 and 86.
02:19
So to get a more exact value, i believe you need to find your z score.
02:23
Okay.
02:24
So i just cut a little snippet of our z score table...