00:01
In your question, you're told that sat scores are normally distributed with a mean of 1 ,500 and a standard deviation of 300.
00:08
An administrator at a college is interested in estimating the average sat score for first -year students, so they want to take a sample of first -year students, and they want to create a confidence interval such that we have a margin of error of 15 points.
00:24
Points.
00:25
Your job in this question is to determine how big of a sample, how many students this sample should include so that we can get that margin of error with that level of confidence.
00:38
So we have the margin of error formula, which is to take your critical value, which is based on your confidence interval, times standard error.
00:50
Now your critical value here, we would call that a z star and your standard error formula is to take a population standard deviation which is why they were given us this standard deviation and divide that by the square root of your sample size that's going to equal your margin of error now we want the margin of error to be 15 so i replace margin of error with 15 the z critical value that's the one thing we have to figure out here that's not given.
01:22
It comes from a normal distribution, and it's the z -score at the upper boundary of the middle 92 % of the data.
01:33
Now, this is not a common z -score that we would have memorized, so we have to do a little work to find it.
01:41
Basically, there's 8 % left for the two tails, 4 % in each, and now what you do is combine these two, and i'll use a program called inverse norm, which finds z -scores based on area.
01:59
So it's going to give me, i want to use the area up to that z -score, which would be 96%, or .9601.
02:10
Now on my ti -84 calculator, that's found under the second distribution key.
02:14
Key...