00:01
All right, so we're doing some work with the normal distribution here.
00:07
And we're rounding c to two decimals and our final p values to four.
00:13
So with the probability that x is less than 23, given the mean is 27.
00:19
The standardization is three.
00:22
So our z score formula is the following, x minus mu over sigma.
00:30
So we substitute in these three values.
00:37
3 minus 27 is our mean.
00:40
Simons are 3.
00:42
And just get a picture for what we're doing.
00:44
So here's a normal curve with the mean of 27 here.
00:51
And we're going to find that probably the x is less than 23.
00:54
Let's see.
00:55
Here's 23.
01:05
There we go.
01:06
Little pendrils there.
01:07
We want the area to the left of 23 because we're looking for x less than that.
01:15
So we get the z score.
01:17
It ends up being negative 1 .3 repeating.
01:21
This is the value.
01:25
This column is filled the values that my spreadsheet gave me, whereas if i rounded these are the values i get because i use my spreadsheet to get all the values.
01:32
So it's just a little quicker.
01:34
But due to rounding, if you round the z score to two decimal places, you can see it's a little different, but not much.
01:45
But for our purposes, in terms of the precision we're asking for, so we'll go ahead and do that.
01:52
And the left area.
01:54
So we just do a table lookup.
01:56
You should get at least the same value for.
01:58
Most z tables give you up to two decimal places, so it should be good.
02:05
So the answer for a left area is 0 .0 .0918, running to four decimal places.
02:23
And before we move on, the area here, this number is the error to the left.
02:29
And most z tables, like my spreadsheet, gives you the area to the left.
02:33
Whereas here for b, we're going to look for the area to the right.
02:36
So we have to do a little extra work.
02:39
This is one extra step, it's not much, but it's a good thing to visualize.
02:44
So here's our mean of 60.
02:48
We want 79, which is right here.
02:50
We want the probability of x is bigger than equal to 79.
02:53
So the symbol doesn't play an issue or it doesn't have any bearing on a work here because this is continuous.
03:01
So we're just going to the difference between greater than strictly than versus greater than equal to.
03:13
This doesn't have any difference here.
03:16
But if it's discrete, then we then that becomes an issue.
03:19
But it's not so we're good.
03:22
So we do the same z score or calculation here except we get different values.
03:33
Maybe 7 is the sigma.
03:35
60 is our mean.
03:36
79 is our x value.
03:38
We get the z score, 2 .71.
03:42
And we do the area to the left, do a table lookup.
03:46
So this is where i'll show this.
03:48
So we don't the probability the x is bigger than that...