00:01
Once again, welcome to a new problem.
00:03
This time we're dealing with standard normal distributions.
00:06
We're dealing with standard normal distributions.
00:12
And when it comes to standard normal distributions, we have a mean which is in the middle and a standard deviation.
00:23
Within one standard deviation of the mean, we have a z of 1 and a n.
00:31
Negative 1.
00:33
So this represents 68 % of the data and then within two standard deviations of the mean, we have 2 and negative 2.
00:46
So this represents 95 % of the data.
00:54
And then finally within three standard deviations from the mean on both size of the distribution.
01:00
This represents 99 .7.
01:03
Percent of the data.
01:06
To get the z score, we use x minus mu over sigma.
01:12
So we use x minus me all over sigma.
01:17
So that's the information that we use.
01:22
And we're looking at a new problem involving crime rates from 24 states.
01:29
And the mean is 3 ,331 in the standard deviation is 729.
01:36
So the first thing we want to do is to determine the property crime rate for the lower 16%.
01:46
So we want to determine the value that represents the lower 16 % crime rate.
01:55
So in that sense, we're saying that there is a value x, which we're going to call the bottom 16, that's less than a certain x, which gives us a probability of 0 .16.
02:12
So if you look at the distribution, if you look at the distribution, the middle on z is 2 and z is negative 2, this represents 68 % of the data.
02:31
And then the balance on both sides of the distribution is given by, so, so this balance is given by 16%.
02:39
And this other balance is given by 16%.
02:42
So we're looking at a z score of negative 2.
02:48
And in that case, we can say that the probability that z is less than negative 2 is the same as 0 .16.
02:57
So that's the probability that z is less than negative 2.
03:04
So x .16 minus mule which represents the z score and of a sigma that z score gives us negative 2.
03:20
And so if you want to compute the actual value of x, you can see that we have negative 2 times sigma plus mu, which is negative 2 times sigma.
03:31
If you go back, you see it's 729.
03:35
And then mu is given by 3331.
03:40
So 3331.
03:44
And so we have 729 times 2 and then minus 3331.
03:54
So we get a crime rate of 1873.
04:02
That's the crime rate you get at that level.
04:10
If we have, so let's see, if you have, the next question is, but b, we're looking at the top 2 .5%.
04:39
We want to get the score for that.
04:41
So in put b, if you're looking at the top 2 .5%, that's right here...