00:01
In your question, you're working with the sampling distribution of a sample proportion.
00:05
You're told that the population proportion of female heart transplants, patients who will survive at least three years, is 78 percent.
00:15
So i've labeled that as 0 .78.
00:18
You're told that a sample of 90 was taken, and we're trying to find what is the probability that the sample proportion, which is the symbol p -hat, is less than 72 percent or 0 .72.
00:31
Okay, so you're assuming that the sampling distribution of sample proportions is a normal distribution.
00:37
That is being stated, but there's enough information here to know that that would be the case.
00:43
It looks like you might be being asked to label the mean of your sampling distribution of the sample proportion, which will just equal the mean of the population proportion, which is the 0 .78.
00:57
And then you're also asked for the standard deviation of the sample proportion, which is the square root of p.
01:09
Now i can see there that you have q.
01:11
Q is just 1 minus p.
01:13
So i'll write q down, but just so you know that q is 1 minus p, and we're dividing that by n.
01:20
So we're going to end up with the square root of 0 .78 times 1 minus 0 .78, which is 0 .22, divided by 90.
01:31
And this works out to be 0 .0437.
01:40
Now i'll keep all my decimal places for when we use that in our further calculation.
01:47
All right, so the actual question is finding this probability...