00:02
I've already drawn us our normal distribution with the mean at 77 .5 right in the middle and a standard deviation of 12 .5.
00:11
Now, the rest of these questions are going to deal with the empirical rule.
00:15
The first question about what scores would encompass the middle 95 % of the scores, that would be two standard deviations above and below the mean.
00:28
So from 52 .5 to 902 .5 encompasses the middle 95%.
00:38
For the next question, what percent of scores are less than 65? so i'm going to find my 65 on my bell curve.
00:50
So essentially, we want to know what percent is shaded in here of the bell curve.
00:56
Well, we know from the middle to the left is 50 % of the scores.
01:06
Now, one standard deviation above and below the mean, 65 to 90 encompasses the middle 68%.
01:15
So that would mean the distance, this part from 65 to 77 .5 would be half of 68, which is, of course, 34.
01:31
So if we know it's 50 all the way to the middle, 34 from the middle to 65, that means there is 16 % left for less than 65, 50 takeaway 34.
01:49
I'm going to skip ahead to letter e just for a second because it'll be easier to do that one before some of the other questions.
01:59
So for letter e, we want to know what percent of the time does that? the score come out to be more than 102 .5, or more than 102 .2...