00:01
For this problem, to begin, we are told that 2 ,500 students take a college entrance exam.
00:08
So we have presumably sample size 2 ,500.
00:12
We have a sample mean, or pardon me, population mean, of 52 points, a population standard deviation of 11 points.
00:20
And we're asked to use the empirical rule, also known as the 68 -95 -99 .7 rule, because it tells us that we expect 68 % of values, within one standard deviation of the mean, 95 % within 2, and 99 .7 % within 3 standard deviations.
00:38
Now for part a, we're just asked to estimate the average score.
00:44
Well, the expected value of the score would be equal to the population mean.
00:49
So we would expect the average for the 2500 to be 52.
00:55
Then we want the percentage of students scoring between 41 points, so percent between 41 and 63.
01:08
I'll note that 41 is 52 minus 11.
01:12
So that's the mean minus one standard deviation.
01:15
And 63 is 52 plus 11.
01:18
So that's the mean plus one standard deviation.
01:20
Using the empirical rule, then, we would estimate that as being roughly 68%.
01:25
For part c, we want the percentage of students scoring 52 points or more...