Dispersion of the normal distribution

Mean value of the normal distribution

Middle value in the normal distribution

Standard deviation of the normal distribution

little higher than if you do it, uh, orally. So we looked at this histogram before.

We already talked about this example earlier in class, but now it's in the content of normal distribution so let me take a second to show this to you.

So, we're just looking at frequency on the y axis.

And, there's a standard deviation of the distribution of sample means, standard air.

Value to which the standard normal distribution is calculated

The number for which the standard normal distribution is to be calculated

Finally the shape of this distribution of sample means will be approximately normal even if the distribution in the population isn't normal.

Then we know a lot about that distribution.

So first let's revisit this normal distribution.

Putting it in population parameters, but putting it in sample statistics.

So a T distribution looks very similar to a normal distribution but it has fatter tails.

Thus, I suspect that each of these examples was distributed according to a normal distribution or

So I can get any value less than 20 given this distribution.

So we know the risks we're running for a type one error and a type two error, as researchers.

The number for which the integral value of standard normal distribution is to be calculated

With that said, let's play around a little bit with this normal distribution.

So this is a cumulative distribution function for the same... for this

less fluctuation in those sample means. So then, if I plotted all my sample means.

Here, I said samples equal to 30 or greater, some people would be a little more liberal then that and say if you have samples of even twenty or greater you'll get a normal distribution.

If you remember from lecture two when we started to talk about probability, we can use the normal distribution.

I mean, a distribution of scores in a sample on some variable.

Everything we do or almost everything we do in inferential statistics which is essentially, making inferences based on data points, is to some degree, based on the normal distribution.

This distribution is also standardized into a Z distribution, which I'll get to in a minute.

look at everybody in the distribution.

Of 100. Now it's looking pretty close to the population.

In this video, I'd like to talk about the Gaussian distribution, which is also called the normal distribution.

It was, they were all over the place.

You don't do this for this relatively complicated expressions over here.

This is from the counter table with very large interval here, so we can use a Gaussian approximation.

Just very, very basic probability. And that'll prepare us for inferential statistics.

Where we assume that 30 wine experts rated the overall quality of four different wines on a scale of one to ten, and ten is highest quality.

So, this script's end stands for normal, since Gaussian and normal distribution, they mean the same phase of synonymous and a

I used this as an example back when we were talking about histograms and descriptive statistics and I showed you this histogram.

And, again we don't know most, most of the time if the distribution in the population is normal.

I am skipping that now because we've done it previous examples, you've done it in previous assignments.

We have 14, was the peak in that histogram.

We would lose that if we just looked at

Just coincidence that beta's used for both of those. Okay.

Otherwise, it would be almost impossible to compute.

We just do it for the normal distribution that I think several could be easy to compute.

That's exactly what we're going to do in inferential statistics.