00:01
Hey there, welcome to numerade.
00:03
So we are asked to describe the sampling distribution of p -hat, given our sample size, population size, and population proportion.
00:14
So with this, we are looking at the mean and standard deviation.
00:22
So what we know here is that the mean of the sampling distribution, so p hat equals the population proportion itself, so p, which equals 0 .78.
00:47
Now for our standard deviation here, we have sigma, subscript p hat equals, all right, so we have equals the square root of the proportion times one minus the proportion.
01:28
Proportion divided by our sample size.
01:40
Okay, so with this here, we get a standard deviation of around 0 .0131.
02:09
All right, awesome.
02:13
So now let's move on to our probabilities.
02:17
For our probabilities, we want to see the probability of obtaining x equals 810 or more individuals with the characteristic.
02:26
So we can set up our z square equation.
02:31
So 810 will be over the 1 ,000, right? and we know that that will just simplify into 0 .81.
02:49
Okay, so we have 0 .81, subtracted to the population proportion of 0 .78, and divided by our standard error or our standard deviation, which is 0 .0 .0.
03:14
131.
03:28
All right.
03:30
Let's see what we get here.
03:33
So we have 0 .81 minus 0 .78.
03:43
Okay.
03:44
Divided by the standard error.
03:47
Giving us a z score of around 2 .29 in which we can find our probability.
03:55
So the probability that x is greater than or equal to 810 will be equal to...