00:01
Suppose that teachers in private schools have an average annual income of 51 ,000 tl and a standard deviation of 1300 tl.
00:18
If a random sample of 100 teachers is chosen, find the probability that the sample mean is greater than 51 ,300 tl.
00:31
Right? so, to find the probability that sample mean is greater than 51 ,300 tl.
00:41
Right? so, for that, we can use central limit theorem.
00:46
Right? central limit theorem is used here.
00:49
Right? and the properties of the normal distribution.
00:57
This is basically the key concept of this problem.
01:00
Right? now, population mean mu is equal to 51 ,000 tl.
01:07
So, this is the basically the annual average income.
01:12
This is given by population mean mu.
01:14
Now, population standard deviation is sigma which is equal to 1300 tl.
01:20
Right? now, sample size is 100.
01:23
So, we want to find the probability of the mean.
01:28
Probability of sample mean being greater than 51 ,300 tl.
01:35
Now, we know the standard deviation of the sample mean is also known as the standard error.
01:42
Right? that is given by se.
01:44
Right? now, sigma x also.
01:47
It is represented by sigma x also.
01:50
So, now which is equal to the population standard deviation divided by the square root of sample size.
01:56
So, this is the formula for that standard error.
02:00
Right? so, now it is we know that sigma is equal to 1300...