And finally, almost all, 99.7%,

of the observations fall within three standard deviations of the mean.

So almost all the distributed points in a normal curve fall within plus or

minus three.

There's a very small percentage beyond three standard deviations in either

direction.

Now technically speaking in a true normal curve, which again,

is a theoretical distribution.

The tails go on forever meaning that there are very few percentage-wise

observations ,that fall beyond three standard deviations.

But technically they can be any value on the real number line.

In real life no data has infinite range, so we'll see that the normal

distribution is only an approximate model for some types of real data.

So what does this mean though?

Let's go back to the 95% plus or minus 2 standard deviations thing,

because this will be what we use most often in the course.

So if we look at this and parse it similar to what I did before, but

talk about things in terms of percentiles.

The middle 95% of values in the normal curve fall between the mean

minus 2 standard deviations and the mean plus 2 standard deviations.

So that means, as we said before, that 2.5, if 95% is in the middle,

the remaining 5% is equally split between the two extremes.

2.5% of the observations that follow a normal curve are smaller than and

then hence the remaining 97.5% is greater than a mean -2 standard deviations.

On the flipside, 97.5% of the values are smaller than, or less than or equal to,

and hence 2.5% of the values are greater than the mean plus 2 standard deviations.

So this mean minus 2 standard devs gives us the 2.5 percentile,