00:01
So we're looking at resting heart rates of healthy adult men.
00:05
And we've got a bunch of different situations here.
00:09
And we want to figure out different percentages of men who would fall into these different categories.
00:14
So the first thing we know is that the mean resting heart rate is 73 .4 beats per minute.
00:24
And the standard deviation is 5 .9 beats per minute.
00:30
Per minute.
00:32
Now, it's worth noting that as we go through each of these, there's six different ones here that depending on where you go to look for your your z values, whether that's a z table or some calculator, the percentages that you come up with might be slightly different, like hundreds of percent different, like, 10ths or hundreds of percent different, like, sorry, tenths or hundreds it's percent different as compared to what i what i'm finding looking at a z table.
01:06
But that's this has to do with like how fine of an answer are you are you calculating? so let's get started.
01:13
We know that the relationship between to find our z values is the relationship between any value that we're looking for, we'll call it x and the mean.
01:25
So that that difference divided by our standard deviation.
01:28
Once we have that amount, that will tell us, when we look at a z table, the amount of, sorry, the probability of that value being on our curve or from the left tail.
01:51
So here's our mean and our x value we can put anywhere.
01:56
It doesn't really matter.
01:57
We'll say it's here for now.
02:01
And when we find our z table from the z value and look at our z table, it'll tell us this amount here.
02:09
That's our, that's our percentage.
02:12
If we want to find it the other side, then we have to do one minus that amount because we're looking at all the green here.
02:23
We would do one minus whatever that percentage is because we know that underneath that normal curve it's going to be 100 % of the data.
02:35
So there's our process.
02:37
Let's go ahead and jump right in.
02:40
For the first situation, we know that we're looking for the percentage of men whose heart rate is greater than 80 beats per minute.
02:50
So to find this, we're going to find our z value, which is 80 minus 73 .4 divided by 5 .9.
03:06
And that's equal to 1 .12.
03:11
1 .12 gives us on our z table a value of 0 .8686.
03:20
But because we're looking for greater than 80 feet per minute and not less than, this is where we're going to use that subtraction.
03:28
So we have 1 minus 0 .8686.
03:35
And that gives us our value, which is 0 .1314 or we could say it as 13 .14%.
03:48
So 13 .14 % of 13 .14 % of men would fall into this range of having a heart, resting heart rate of over 80 beats per minute.
04:01
All right, let's take out the second one.
04:02
Second one, we're now looking at what percent of men are in between 70 and 85 beats per minute.
04:13
So we have two to look at here.
04:15
Same exact process.
04:17
Look at our 85, 85 minus 73 .4, divided by 5 .9.
04:25
And that ends up getting us a z score of 1 .97.
04:32
And compare that to 70.
04:35
So 70 minus 73 .9.
04:39
I'm sorry, 73 .4.
04:43
In my own handwriting mixed up, 73 .4 divided by 5 .9.
04:49
And that gets us to negative 0 .58.
05:02
So the z value going to our z table, 1 .97 is the same thing as 0 .9756, so it's most of the data.
05:17
And for negative 0 .58, it's 0 .28 .20.
05:24
So to find the percentage of men who are in between here, we have to subtract them because they're basically overlapping.
05:30
So we take .9756 and we subtract .2810.
05:39
And what we end up with is .6946 or 69 .46 of the men will fall into that range.
05:55
And again, why this works, just to think about it in terms of our graph, just to write it out briefly.
06:04
Here's our mean again.
06:05
So for the first value at 85, so 85 would fall somewhere over here, 1 .97...