00:01
All right, so we're told that this one measurement for these sea turtles is 98 centimeters and that it has a standard deviation of 12.
00:13
But we're going to take a random sample because we don't know that.
00:16
So we're going to take 36 sea turtles.
00:21
Okay.
00:22
First question asks, what is the mean of the sampling distribution of x bar? so the mean of the sampling distribution is always going to be equal to the parameter from the population.
00:35
So the main of the sampling distribution of x bar is going to equal mu, which is 98 centimeters, right? so that is the mean of the sampling distribution.
00:47
For number two, the stern deviation of the sampling distribution is going to be sigma divided by the square root of n.
00:56
So in this case, that is 12 over the square root of 36.
01:00
Squared of 36 is just 6.
01:02
So it's just 12 divided by which is 2.
01:05
Okay, so the standard deviation of the sampling distribution is 2, which is also called the standard error.
01:16
For the third one, it asks what is the shape of the sampling distribution? it's going to be approximately normal because we have an n greater than 30, with a mean of, we just figured it out, right, a mean of 98 and a standard deviation of 2.
01:41
We just figured out that.
01:43
For number four, it says to find the probability that the mean from my sample is less than 96.
01:53
So to do this, we're going to take a z score.
01:57
It'll be x bar minus mu over the standard error.
02:01
So it'll be 96 minus the mean from the population 98, divided by the standard error, which is 2.
02:09
So we just get negative 1.
02:11
That is my z score, right? so when i look up my z score of negative 1 here, i need to get, let's see, i'm looking for the probability that it's less than that, right? so i need this area right here.
02:27
So i'm going to look it up, and i get 0 .1587 for that probability there.
02:38
Okay? okay, so for the second part of this, we have this sample that we took of 36 turtles, and the sample mean was 99, and the sample standard deviation was 16.
03:01
So first thing is, what is the point estimate of the population mean? there's not really any work to show on this, because the point estimate of the population mean is just the sample mean...