00:01
So we have a normal distribution with a mean of 57 ,800, standard division of 750.
00:11
First part of the question is to find the probability that the random variable of x is between 57 ,000 and 58 ,000.
00:33
This is a normal distribution.
00:35
So this is just going to be 57 ,000 minus 57 ,000 800, standard division, 750.
00:50
This is x minus here, over standard division, this is going to be 50, 800.
01:00
Just a second, this is 58 ,000.
01:05
This client is up.
01:12
Minus 57, 800, over 750.
01:21
So let's see.
01:27
So, let's see how big and divided by 750.
01:35
This will be negative 1 .07.
01:40
And this is going to be, let's see, 1 divided by 750, 0 .27.
02:02
Okay, this becomes probability of z less than 0 .27.
02:11
27 minus probability of z then negative 1 .07.
02:21
Alright, so we're going to use the z table to figure this out.
02:30
Okay, we're going to look for the probability when z is 0 .27.
02:37
So when we have 0 .27, our probability is 0 .60 -442.
02:50
0642 and i'm in z so we have to make this negative 1 .1 so for negative 1 .1 probability is 0 .13567 1357 so let's look at the required probability here so 0 .60642 minus 1 .135 67.
03:25
7 .5 .0 .4705.
03:36
Let's go to 2.
03:39
We need to find a mean and standard division with a sample size of 100.
03:45
So for a sample size of 100, the mean, what a sample mean? it's always equal to the population mean.
03:53
And that is still 57 ,800.
03:59
The standard division, however, is going to be the population standard division divided by the square root of it.
04:09
N, okay? so let's see that's 750, divided by a square root of 100, that is 10, so that is 75, then 3...