00:01
We're looking at a normal distribution, and we are using the empirical rule.
00:06
So i'll start by explaining what that is.
00:09
I'll draw out a normal curve.
00:16
There we go.
00:17
Okay, so 100 % of the scores are underneath this curve, and it's symmetric.
00:24
So half are below the mean, half above the mean.
00:27
And if i mark some lines on here, these are going to represent values a particular number of standard deviations, above and below the mean.
00:38
So this is the mean.
00:39
This is one standard deviation above, two and three.
00:44
One standard deviation below, two and three.
00:48
And the rule we're using is the empirical rule, also called the 68, 95, 99 .7 percent rule.
01:00
It's giving you the approximate percentage of scores within particular intervals.
01:06
So for example, 68 % is within one standard deviation of the mean.
01:13
So it's between minus 1 and 1.
01:15
95 % within 2, 99 .7 % within 3.
01:23
And this works for any distribution that is unimodal and symmetric.
01:29
So normal, approximately normal, bell -shaped, any of those.
01:35
Part 1, we want to know the interval for 95%.
01:38
So we need the mean, mu, minus two standard deviations, and the mean plus two standard deviations.
01:47
Mean is 75 .23, sigma, 7 .89.
01:54
So i'm just going to do 75 .23 minus two of these, and that will get me the lower limit here, 59 .45, and the upper one is 91 .0.
02:10
Rule.
02:12
So that's the interval for 95%.
02:14
That's this interval here.
02:18
Part two.
02:25
Okay, the precise rule.
02:26
So this was would be empirical rule...