I am using Mathematica 8 for my stat class... I am completely lost. Just too old to be taking a math class. I need to find someone who can walk me through solving a couple of problems. It is important that I understand this before I move on with the class. Here is the first (3part) problem:
National SAT math scores have a mean of 514 and a standard deviation of 113. Assume these scores are normally distributed. All LLCC students must take a placement exam unless their math score exceeds 480. Estimate the percentage of students that must sit the mathematics placement exam. Find the 95th percentile. Interpret this result in the context of the problem. A sample sizze of 100 is taken from the population. Find the probability the sample mean is less than 494.
Second problem:
A studen has essay scores in composition course of 98, 78, 82, 88, and 79. The grade in the course is dertermined by random selection of 3 essay scores. Find the probability that a sample mean of size 3 will be within 5 points of th population mean.

Please Help

1. So, you need to get the proportion of students having scored less than 480.

So, you are looking for the probability of getting a student with a score less than 480.



This is the formula you need to use, that is, you need to find the z-value. Mu is the mean, sigma is the standard deviation, x is 480. Once you get the value of z, you will use your z-table and look for the probability corresponding to that z value.

When you get the probability, you can get the number of students using the expectation formula, that is np (where n is the total number of students and p is the probability that you just got.)

2. You obtain this going backwards here. From the probability of 0.95, find the z score and use the formula again to find x.

i.e..

3. I'll leave that for you to give it a try :)

4. Okay, that I've not done in my courses, but my book nevertheless covers that part. I'll have to see that and then I'll post back (as well as the last part). But mind you, I have no experience in those two last questions though.

For the last problem - it's easiest to figure out how many combinations of scores fall outside the +/- 5 point range. If you can find the probability of selcting 3 tests that have a mean that falls outside the range, then the probability of selecting 3 tests that fall within the range is 1 minus that.

a. You can calculate the mean and the range that is within 5 points of that mean. Then check for various combinations of scores that are either higher or lower than that range, and call that number 'a.'. For example: the lowest 3 scores of 78, 79 and 82 have a mean of 79.67, which is more than 5 points below the mean of all 5 scores. Next you would check the combination of 78, 79 and 88, etc. Don't forget to also check the combinations of the highest scores to see if any of them exceed the range.

b. Once you figure out how many combinations fall outside the +/- 5 point range you need to determine how many possible combinations there are for selecting 3 tests out of a population of 5 - do you know how to do that? Let's call that number 'b.'

Finally, the probability you're looking for is 1-a/b.