00:01
All right, in this question, we're looking at blood pressure.
00:04
And blood pressure is normally distributed with a mean of 122 and a standard deviation in 19.
00:11
So automatically we can draw that funky standard normal distribution here.
00:17
In the middle goes the mean.
00:19
So you put a value of 122 here.
00:22
And then up and then you have a standard deviation of 19.
00:26
So you count up one standard deviation, two, and three.
00:30
And then you count down.
00:32
By 19, takeaway 19, takeaway 19, takeaway 19.
00:35
What i mean is you add 19 to get this value.
00:38
You'd add another 19 to get that value.
00:40
For the second standard deviation, you add another 19 to get a third standard deviation.
00:45
It tells you how the data is distributed.
00:48
Well, let's read through a little bit more here.
00:50
It says that you have stage 2 high blood pressure if your blood pressure is 160 or higher.
00:57
So let's stick 160 in here.
00:59
Where would 160 be? let's see.
01:00
If i took 122 and added 19.
01:05
So here's one here at the first standard deviation.
01:11
141.
01:12
Let's add 19 again.
01:15
The second standard deviation is 160.
01:17
So 160 is actually two standard deviations above the mean.
01:22
So 160 has a z score of 2.
01:28
It does ask around what percentage of adults in the u .s.
01:31
Have stage 2 high blood pressure or above 160? so we're looking at 160 here and want to know what the percentage, what the area under the curve here or what probability would give me higher than 160.
01:47
So to do this with any number, it just so happens that 160 is one standard or two staring deviations.
01:53
What you want to do is find the c score.
01:55
So you would take your number 160, take away the mean, and then divide it by the standard deviation.
02:01
We get two.
02:02
Now there's a lot of different ways to find this probability here.
02:05
This little area under the curve.
02:10
One way is to use an online calculator, another way is to actually use your calculator.
02:15
So what we're looking for is a graph that would be, you know, this, it would look like this.
02:20
So we're shaded for that little bit of it.
02:22
So we're looking at this one right here.
02:24
So this calculator tells me that the probability is of greater than 160.
02:29
It's 02275.
02:33
Now if i use my calculator, if i have a basic, graphing calculator we hit vars sorry second vars number two and we're looking for you put your you put the lower which would be two a z score of two and we want to go further out to infinity so i put comma 9999 and then i'm gonna close it here and it would tell me the same number 02275 so that's how i get my probability now if we're looking at part b, it's my probability i've got it.
03:15
0 .0255 of that thing.
03:17
Part b is asking if you sample 2 ,000 people, how many would you expect to have that higher than 160? so we'll take that probability.
03:32
We'll take that probability here.
03:35
We're going to multiply it by 2000.
03:38
So approximately round up be 46 people, 45 .5 or 46 people.
03:48
Part c, stage 1 high blood pressure is specified between 140 and 160.
03:56
So 140 is right here, right below that first z score.
04:02
So let's find the z score for that.
04:03
Remember how we do that...