We went one standard deviations, two standard deviations.

So they're all well documented deviations from rational behavior.

So how many standard deviations away from the mean is this?

How many standard deviations.

It's 1.9 standard deviations.

More than 3 standard deviations.

So this result right here is 3 standard deviations away from the mean.

Essentially figure out how many standard deviations away from the mean this is.

We know the area between minus three standard deviations and plus three standard deviations.

So let's figure out how many standard deviations away from the mean that is.

This tells me how many standard deviations is minus 20 away from the mean.

So let's figure out how many standard deviations we are away from the mean.

So this is 2.58 standard deviations.

3 standard deviations below the mean.

This is two standard deviations below.

This is two standard deviations above.

If we do our standard deviations, to the left that's one standard deviation, two standard deviations.

That's two standard deviations below the mean and 11.7, one, two standard deviations above the mean.

Remember, z score is just how many standard deviations you are away from the mean.

Or this is equivalent to being 2.34 standard deviations away from this mean of 0.

A z score is literally just measuring how many standard deviations away from the mean?

If I did 1 standard deviation, 2 standard deviations, 3 standard deviations that's in the positive direction.

And we are 2.35 standard deviations away.

And then we have 1 standard deviation, 2 standard deviations, and 3 standard deviations in the negative direction.

If you go two standard deviations, it's going to be 2, three standard deviations 3, just like that.

If we're looking from this point to this point, so it's within two standard deviations, right?

Or 2.5 of the samples from this population are going to be more than 1.96 standard deviations away from the mean.

1, 2, 3 standard deviations below the mean.

We were 2.5 standard deviations below the mean.

But a z score literally just means how many standard deviations you are away from the mean.

So this whole term right here is how many standard deviations we are away from the mean.

Well we go from the empirical rule that 99.7 of the probability is within 3 standard deviations.

So they want to know what's the probability that we fall under this area right here, or essentially more than two standard deviations from the mean, or above two standard deviations.

This tells us that at 2.5 standard deviations above the mean, so this is 2.5 standard deviations above the mean.

So another way to think about think it, think about how many standard deviations we need to be away from the mean, so we're going to be a certain number of standard deviations away from the mean such that any sample, any mean that we sample from here, any sample from this distribution has a 99 chance of being plus or minus that many standard deviations.