00:01
Hey there, welcome to numerate.
00:03
So we have 1 ,184 observations for this normally distributed random variable.
00:11
So we're asked to find a mean and standard deviation.
00:15
So what you will learn here is that the mean, which is basically equivalent to mu, subscript x bar for the sampling distribution, we have this equals to the population mean, which is given to us.
00:41
So therefore our mean is actually our population mean here, which is 8 .69.
00:53
All right.
00:54
So we're going to round to two decimal places.
00:56
So now for our standard deviation.
01:01
Now for our standard deviation, this will be equivalent to sigma, subscript x bar.
01:10
So this is basically equivalent to the population standard deviation divided by the square root of our sample size n.
01:20
So we plug in our values here.
01:22
We have 0 .84 for our population standard deviation.
01:28
And our sample sizes the 1 ,184 observations.
01:34
So let's see what we get here.
01:36
0 .84 divided by the square root of 1 ,184.
01:46
0 .84 divided by the square root of 1 ,184, giving us a standard deviation of around 0 .02.
02:00
All right, now we are asked to find the number of observations.
02:05
So this is basically the probability that the, so this looks like is the sample mean, is less than 8 equals.
02:23
So in order to find us, we would have to set up a z score equation.
02:27
We take our mean 8 .69 and subtract it to our, sorry, we take our 8 minus our mean of 8 .69, which is divided by the standard deviation of 0 .84, divided by the square root of our sample size here, which is 1 ,184.
02:53
So we already found the 0 .02 for the denominator...