00:01
In this problem, we're going to be looking at a sampling distribution and then using the aspects about a sampling distribution to find a probability of obtaining a given sample.
00:12
So the first thing we need to do is we need to clarify what are the characteristics of our sampling distribution.
00:18
And based on the information that's given, we know that the center of our sampling distribution is going to be 0 .8.
00:25
Okay and again that is true because we have a simple a simple random sample of size 75 since it is random we expect it to be not biased so pretty close to that population proportion the next thing is the shape of our sampling distribution is it approximately normal and it is because the large counts condition is met so it is approximately normal and the the next thing is our spread.
00:59
We need to know our mean, our standard deviation, and then the shape.
01:03
And our standard deviation for this particular sampling distribution worked out with the formula shown below is .046, which we know is true because our population size, 10 ,000, is greater than 10 times our sample size.
01:25
That's the independence condition.
01:26
The standard deviation hinges on that independence condition.
01:30
So now that we have the information we need, we can actually calculate our probabilities.
01:36
So we have a normal curve, and it is centered at 0 .8.
01:44
And for the first part here, we are looking for what is the probability of obtaining a sample that is 0 .84, greater so that's what it would look like and the easiest way of doing that is to use our normal cumulative density function on our calculator with our low limit being 84 our upper limit being one because you can't have a proportion higher than one you could use 1 ,000 or infinity or whatever it would give you the same answer but speaking in context of the problem one is what we want our mean is 0 .8 and our standard deviation is 0 .046...