00:01
In this question we are looking at a normal distribution, so i'm going to draw one.
00:08
The total area under this curve is 1, or 100%.
00:11
It's a probability curve.
00:13
It's also symmetric.
00:15
The probability of our observation x being below the mean is 0 .5, above the mean 0 .5.
00:22
The mean, mu, is 50.
00:25
The standard deviation, sigma, is 7.
00:28
We want to find the probability that x is greater than 38.
00:34
Now 38 is below the mean.
00:39
We want greater than, so we want the area to the right.
00:45
Now there is a function that takes you from a value on this curve to the area under the curve, but it is extremely complicated.
00:53
You would need to do some high -level calculus to find this, and we just don't do it by hand.
00:59
You need something that has the normal distribution built into it.
01:03
So before everybody had a calculator, you'd be using a z -score table, and sometimes they still ask you to use one...