00:02
Okay, so this question has to do with sampling and population means.
00:06
So we know that for the first one, they want us to find the sample mean.
00:12
So we know that the sample mean is actually the same as the population mean.
00:17
And the population mean is given to us as 400.
00:20
So here, the sample mean is going to be 400.
00:24
As for the standard deviation, the sample standard deviation is, sorry, sorry.
00:31
The sample standard deviation is actually the population standard deviation divided by the radical of the sample size.
00:39
So here the population standard deviation is 50 and the sample size is 25.
00:49
So it's going to be 50 divided by 25, which is a radical of 25 which is 5.
01:00
So standard deviation is going to be 10.
01:05
Okay.
01:06
Find the probability that x bar is less.
01:08
Than 390 so we're doing fine the probability that x bar is less than 390 so we are going to convert that into z scores so we're going to get set less than 390 minus 400 divided by 10 when we do that we get negative 1 now we go back to our normal distribution tables so it's 0 .15866 so 0 .15866.
01:44
So that's the probability of the average being less than 390.
01:51
So find the probability that x is between 405 and 425.
02:09
So basically we're looking for this.
02:15
So our average is 400, 405 would be here...