00:01
Okay, so we have a population as a mean of 300 and a standard deviation of 80.
00:04
And let's suppose that a sample of size of 100 is selected and used to estimate the population mean.
00:10
And so we want to figure out the probability that sample mean will be within 9 units of the population mean.
00:16
And also, what's the probability that a sample mean will be within 18 units of the population mean? okay, so let's first write down what we know.
00:23
We know the population mean is 300.
00:26
So mu is 300 and sigma.
00:31
Be standard deviation is 80.
00:34
Again, we, it's common to use the greek letters to represent the population parameters.
00:45
So normally distributed, mean of 300, standard deviation 80.
00:49
And we're trying to figure out what's the probability that our sample mean, if randomly selected, it will be within nine units, the population mean.
01:02
So, we're dealing with the sampling distribution of the sample mean.
01:09
So we want to find the probability that the sample mean will be from 291 to 309.
01:27
Because 9 units within 300, you add and subtract 9 to 300, you get 291 and 309.
01:32
So what's the probability that our sample mean will be between 291 and 309? now, we need to also recognize that this could be a different shape, or could have different values.
01:48
So let's define what the population or what the standard deviation and the mean of the sampler distribution of x bar would be.
01:58
So the mean of the standard distribution of x bar is equal to and the center deviation of the standard deviation of the standard distribution of x bar is equal to.
02:05
Now the mean of the sampler distribution of x bar will be equal to the population mean because it's an unbiased estimator, so it's just going to be 300.
02:17
Now the standard deviation of the sample distribution of the sample of the x bar is equal to the population standard deviation divided by the square of the sample size.
02:27
So the square root of 100, or let me just write n and then...