0:00
All right.
00:01
So we have some work with our normal probability distributions, and we're looking for the probability that a randomly selected female will have systolic blood pressure, meaning some parameters.
00:19
So we're given that the systolic blood pressure of females is normally distributed with the mean of 106 .3 and the standard deviation of 8 .9.
00:29
So it's going to be sigma.
00:31
I put sig because my spreadsheet doesn't have a sigma character in it.
00:37
So we'll just add it in there.
00:41
And we want to find the probability that a randomly selected female will have a systolic blood pressure of less than 110.
00:53
So notation -wise, we know the probability that x is less than 110.
00:58
Like this.
00:59
So the way we do this is we convert our x to a x to a, z score x minus mu over sigma in this case the means so for us let's make our formula here x minus 106 .3 divided by 8 .9 so we substitute 110 for x we get this z score and we're told to use a table now when i first did this i just use my spreadsheet to give me the values i use norm s dist and you input your z score and then out pops the air to the left.
01:40
So, um, which is what we want.
01:44
We want points, it ends up being point six six one one nine.
01:49
But i see the note about using the table.
01:53
So not all tables function the same way.
01:58
You always get the same value, but we, they function differently.
02:01
So let me show you how this one that i found works.
02:04
So we get the z score of point 4157, but we're going to round to the nearest 100th, so this becomes 0 .42.
02:14
So the way this table is set up is you read off your 10th place, and you match it up with your hundreds.
02:21
So we have 0 .42, so we go to z .4, we read over to point, and we can point that 2, because 0 .4 plus 0 .02 is 0 .42, and that is the area to the left.
02:34
And this table reads off the area to the left of that z score.
02:39
So you get 0 .66276, which is not the same as what we got here, but there you go.
02:58
So then for b, we want the probability that a randomly selected female will have blood pressure more than 96 .5.
03:05
So this is going to be probability that x is greater than 96 .5.
03:15
So we do the same thing with our z score to put 96 .5 in for x.
03:21
We get the z score.
03:23
We get this negative 1 .1.
03:27
I did the work in the spreadsheet already.
03:34
You can see the answer, but we'll do the table.
03:43
Oh, but notice we want, okay, we want x greater than this value.
03:46
So the way we do this is we actually do one minus the probability of x is less than that.
03:53
96 .5.
03:56
The reason for that is because we just said that the table in my spreadsheet gives us the air to the left, but we want to the right bigger than 96 .5.
04:04
So we do, we look up the z score of negative 1 .1 .0 and we get that left area.
04:14
And then we do the subtraction to get the right area.
04:17
So negative 1 .1 of the table, we go to negative 1 .1 .1.
04:25
The first column is actually with a hundredth is zero.
04:28
So this is the column we want to be in.
04:31
So negative, sorry for the slide screen.
04:33
Negative 1 .1, this is our, that's our value right there, 1 .3567.
04:41
So we do one minus 0 .13567, and we get 0 .867, and we get 0 .86433, which when i did it, 0 .1 ,000 .2 ,000.
05:03
864, it's close, right? so there we go.
05:07
All right, now see, we want the probability that a female will have a blood pressure between 93 and 130 .3...