00:01
All right, and your question, you're told we're looking at quality control.
00:05
We're supposed to assume that the proportion of produced items that are non -conforming is supposed to be 8%.
00:16
So i put that down as 0 .08.
00:19
And we're going to take samples every week.
00:22
A batch of items is evaluated.
00:24
That's a sample.
00:25
And we adjust if the proportion in that sample exceeds 10.
00:31
So what i have done here, in part a, we have a sample size of 74, and i'm looking for the probability that our sample proportion exceeds 10%.
00:45
And that's the same question for both problems.
00:47
You're just changing the sample size.
00:49
Now what we need to do here to calculate this, first we need to understand that a sampling distribution of sample proportions can be considered to be normal if your sample size is large enough, typically over 30, so yours are well over 30, so we would assume a normal distribution.
01:09
Then we're trying to find the area to the right of 0 .1 in both of these models.
01:17
Again, the difference is the sample size.
01:20
How the difference actually takes its effect is in the standard deviation of that sample proportion.
01:27
We use the formula p times 1 minus p divided by sample size.
01:33
Size.
01:34
So if your sample size changes, it causes your standard deviation to change.
01:40
Let's move on to calculating z scores.
01:42
Your z score is going to be calculated by taking your sample proportion minus the mean proportion divided by the standard deviation of your sample proportion.
01:55
So for us, that's going to be 0 .1 minus 0 .08 divided by the square root of 0 .1 .0 .8 .5.
02:07
08 times 1 minus 0 .08 is going to be .92 over our sample size for this first one was 74.
02:17
So that's what you want to type in your calculator...