00:01
There is given a normal distribution, the mean and the standard deviation were given here.
00:06
So the mean denoted by mood, this is equal to 100 and the standard deviation, which is denoted by sigma, that was equal to 10 here.
00:15
So i can define the random variable x, which is normally distributed.
00:19
This is 110.
00:21
Let me just draw the normal term here, and we're going to find the interval for the 90 % of the distribution around the mean.
00:30
Let's say this is mu, which is equal to 100.
00:33
So for the lower boundary, i have x1 and for the upper boundary, which is x2 here.
00:38
Since this x1 and x2 both symmetrical with respect to mean value here, so that means the area of this yellow shaded region should equal to the area of this green shaded region.
00:49
And what we want, the total sum for these two regions should be 90%.
00:54
So that means that each of them would be 45%.
00:57
This one is also 45%.
01:00
45%...