00:01
For this question, there is a standard normal distribution, and we know that the mean value, denoted by mu, should be zero, and the standard deviation, denoted by sigma, that should be one for the standard normal distribution.
00:15
So we can define the random variable z for this distribution.
00:19
This is 0 and 1 here.
00:21
So what am i supposed to do here? first of all, the middle 95, 91%.
00:26
So if i just graph the distribution, we can easily understand what that means.
00:30
This is the normal distribution we have here and the middle 91 percent so let's say this is mue is equal to zero there should be some z1 and there should be some z2 here and the total area which is 91 so these two areas are identical that means the area are equal to each other the yellow and the green one here so the total area is 91 percent so the half of the area which is this is 0 .91 divided by 2 which is this is 0 .45 and this is also 0 .455.
01:12
So in order to get the z1 we have to get the area the the z value is less than z1 so that means we need to just get the area of this shaded region.
01:22
So we know that from negative infinity to mean value the aria was 0 .5 so the probability of z is less than z1 which is equal to 0 .5 minus 0 .45.
01:36
This is equal to 0 .5 minus 0 .45.
01:42
So the value is 0 .045.
01:45
In order to get the z1, i'm going to use the inverse norm function here.
01:49
So the inverse norm from left and right, the area was 0 .045, the mean and the standard division.
01:56
That gives us the value of z1 here.
01:58
So press second variance, the third option here...