00:01
For this question, there is given a standard normal distribution.
00:04
So for this distribution, we know that the mean, which is denoted by mu, should be zero.
00:09
And the standard deviation, which is denoted by sigma, should be one.
00:13
And we can define the random variable z, which is normally distributed.
00:17
This is 0 and 1.
00:18
So let's take a look at the first one here.
00:21
So we have the z value here, which is negative 2.
00:27
So i'm going to graph the bell shape here.
00:29
Let's say this is where the z value is zero so the z is equal to negative two which is this part here so we have to find the total area which is the left of z is equal to negative two which is this yellow region and also we have to find additionally the area to the right of z is equal to two so the z is equal to two which is this place here and the area of this region so the total area here, which would be the probability of z is less than negative 2 and plus the probability of z is greater than 2.
01:07
So we know that this is symmetrical with respect to mean value.
01:10
So negative 2 and plus 2, which is symmetrical with z is equal to 0.
01:14
So i can just write this answer as this is two times the yellow and the green region.
01:19
They are equal to each other, which is two times the probability of z is less than negative 2.
01:24
In order to get this probability, i'm going to use the normal cdf function for the graph and display calculator.
01:29
There is no lower boundary.
01:31
I'm going to put a very small number.
01:32
The upper boundary is negative 2, the mean and the standard division.
01:36
So this is two times.
01:38
Press second and variance, the second option here.
01:42
This is negative 1, second a99.
01:44
And the upper boundary is negative 2.
01:47
The mean value is 0 and the standard division is 1.
01:49
So the answer would be 0 .04 and 15.
01:54
This is the answer we have for part a.
01:58
And what about for part b? so in this case, there is given another 2 z values.
02:05
Let me just graph them first.
02:09
So the z value is given here, which are negative 1 .58.
02:14
This is negative 1 .58...