00:01
We are looking at a normal distribution.
00:02
I'll start by drawing that.
00:05
The total area under this curve is 1, or 100%, and it is symmetric.
00:10
Its mean is 21 .4, with a standard deviation of 6.
00:17
In part a, we want the probability a randomly selected student reading a ct score is below 20.
00:24
20 is below the mean.
00:26
And we want this area here, the probability of falling below that.
00:31
Now, the function you would have to integrate to find this area is too complicated to do this by hand.
00:37
You need something with the normal distribution built into it.
00:40
That could be software, like excel or r.
00:42
I'm going to use my ti -84 calculator with the normalcdf function.
00:49
This has four inputs.
00:51
A lower bound, upper bound, mean, and standard deviation.
00:55
It gives you the area between the lower and upper bounds.
00:59
So i know my upper bound is 20.
01:02
For the lower bound, i recall that the normal distribution never touches the x -axis.
01:07
It just goes on forever.
01:09
So the lower bound should be minus infinity.
01:11
It doesn't really make sense in context, but that's the normal distribution.
01:15
My calculator doesn't have this button, so i put minus 10 to the 99 instead.
01:19
Nearly as good.
01:20
Up to 20, with our mean and standard deviation.
01:26
The output is the solution, 0 .4078, to four decimal places.
01:33
Part b...