00:01
This problem says a set of a thousand exam scores is normally distributed with the mean with 72 and a standard deviation of 8.
00:06
Use the empirical rule to complete the statements below, and we want to complete a bunch of statements that give us how many students score higher than a value between certain values.
00:14
And the way we're going to do that is using the empirical rule, which breaks down our normal distribution in the form we see here where we have certain percentages of our observations falling within a certain amount of standard deviations away from the mean.
00:26
So if our mean here is 72, we have increases of one standard deviation for every section we see to the right.
00:33
So adding one standard deviation would give us 80, adding two would give us 88, and adding three would give us 96.
00:40
If we're going the other direction and taking away standard deviations, we would have 64 from one standard deviation less, and then 56, and then lastly, 48.
00:52
So when we're answering all of our questions, what we can do, since we know that there are a thousand total exams, is just move our decimal place over once from our percentage.
01:03
Because, for instance, if there was 100 exams, we could just keep the number the same.
01:07
But to make it out of 1 ,000 exams, we can just move that decimal place over one time.
01:12
So it's out of 1 ,000.
01:13
So for all of these problems, we're going to use the empirical rule and then move our decimal place over one time...