00:01
We are looking at a normal distribution, so i will start by drawing it.
00:07
The total area under this curve is 1, or 100%, and it's symmetric.
00:13
Half of the scores will be below the mean, half will be above the mean.
00:17
The mean, mu, is 21 .3.
00:20
The standard deviation, sigma, is 6 .4.
00:24
We want to find some probabilities here, so we'll start with a.
00:28
A randomly selected student has a score less than 19.
00:34
So 19 is below the mean, and we want less than.
00:39
So there is a function that will take you from this value to the area under the curve, but it's really complicated.
00:45
Don't do this by hand.
00:47
You need something that has the normal distribution built into it.
00:51
That could be excel or r, some kind of software, or it could be your calculator.
00:57
I'm going to use a ti -84 with the normal cdf function.
01:05
Into this i need to put a lower bound, an upper bound, a mean, and a standard deviation.
01:11
It will give me the area between the lower and upper bound.
01:16
So the lower bound here really should be minus infinity.
01:19
The normal distribution never touches the x -axis, but the ti -84 doesn't have an infinity symbol, so we use minus 10 to the 99.
01:29
Nearly as good.
01:30
Upper bound is 19, so this will give me the area between basically minus infinity and 19.
01:38
Mean, standard deviation.
01:43
So that first part, it looks like you have that correct.
01:46
Yep, 0 .3597...