00:01
And then, let's look at the problem.
00:03
To solve the problem, we can use the properties of normal distribution as we have been given.
00:09
The particular type we invented standard deviation was 75 gpa and 2 .1.
00:19
Let's see.
00:24
The central limit theorem states that the distribution of sampling means from a large enough sample will approximately be normal distributed regardless of the shape of the particular distribution.
00:33
Let's calculate the required properties.
00:35
For the first part, we have to find the probability of 74 being less than or equal to x bar is greater than or equal to 76.
00:43
Then, n is equal to 16.
00:46
The population mean or we can write it as mu is 75 gpa.
00:54
And the population standard deviation is 2 .1.
00:59
To calculate the probability, we need to standardize the value using the formula z is equal to x minus mu divided by standard deviation divided by square root n.
01:14
So, where x is the sample mean, mu is the population mean.
01:17
Standard deviation is the population standard deviation.
01:19
N is the sample size.
01:21
For the lower bound, we will find z lower to be equal to 74 minus 75 divided by 2 .1 under root 16 which will come out to be minus 2 divided by 0 .525.
01:40
That will be minus 3 .8095.
01:44
For z upper bound, we will have 76 minus 75 divided by 2 .1 divided by 2 .525.
01:57
The value of which will be 0 .38095...