00:02
Once again, welcome to a new problem.
00:04
This time, we're dealing with standard normal distributions.
00:13
So we're looking at standard normal distributions.
00:15
And when you think about these distributions, it just so happens that your typical normal distribution has a mean and a standard deviation such that within one standard, deviation of the mean on both sides of the distribution.
00:36
We're looking at 68 % of the data.
00:40
And then within two standard deviations of the distributions, where the z scores happen to be z is 2 and z is negative 2, we're looking at 95 % of the data.
00:58
And then finally, if you spread your distribution all the way up until three standard deviations of the mean, you end up with 99 .7 % of the data.
01:10
The z score is given by x minus me over sigma and the z score tells us the number of standard deviations, the number of standard deviations from the mean.
01:30
So you're saying we have the mean and these are the standard deviations you're looking at.
01:36
We're given a problem where we want to determine the z scores such that 89 % of the data lies between these two z scores.
01:49
So we're going to set up the distribution and assume that the distribution is normal with the mean and standard deviation.
02:00
We don't know what the z score is.
02:02
This is z1 and this is z1.
02:05
2.
02:07
We're given that the middle between these 2 z scores happens to be 89 % of the data distribution or 0 .89.
02:19
And that simply means that the two tail ends would have 1 minus 0 .89 and then divide by 2.
02:29
And so that's going to give us a value.
02:34
So we do 1 minus 0 .89.
02:37
And we want to divide that by 2.
02:41
So we get 0 .11.
02:44
So this tail right here in terms of distribution is 0 .11.
02:51
And so if we want to get the z score for that probability, we're saying probability that z2, probability of z2, z is less than z2 is going to be .11 and also probability that z is greater than z1 is going to be .11.
03:37
So z1, you have to go to the z table, and check what z1 is going to be.
03:48
So z1 will be the same as if you look up on the z table, the z score table, we go back.
04:20
So z1 will be the same as we have to look at.
04:29
So point 11, that's what we're looking at.
04:35
That's going to give us, so 0 .11.
04:40
Let's just say.
04:42
Well, actually it's not 0 .11...