Thread: Question about normal distribution problems

Hello, I'm not sure how to word this as I just started studying normal distribution today but I'll try:

When I do a normal distribution problem, I have to draw a graph. Is it common to simply memorize the areas of each number, like 3.4 for 1 and -1, and .135, .024, etc. rather than referring to the table? I'm not sure if I'm doing something wrong but I seem to get more accurate answers by just memorizing those numbers.

Here's an example of a problem I just did:

The test scores on the quantitative portion of the SAT are normally distributed with a mean score of 570 and SD of 70. Using the empirical rule, approximately what percent of the scores are more than 710?

I used the formula: z = x-mu/sigma

= (710 - 570)/70 = 2

If I use the method of memorizing the numbers and drawing it out using them, I get 2.5% which is the answer the CD for my book has.

(my work = p (z > 2 ) = 0.5 - 0.34 - 0.135 = .025 = 2.5%

If I use the table, it turns out like this:

P (z > 2) = 0.5 - 0.4772 = 0.0228 = 2.3%?

The CD program marks 2.5% as incorrect. Am I doing something wrong? Or are both answers acceptable?

Originally Posted by paperstar

Hello, I'm not sure how to word this as I just started studying normal distribution today but I'll try:

When I do a normal distribution problem, I have to draw a graph. Is it common to simply memorize the areas of each number, like 3.4 for 1 and -1, and .135, .024, etc. rather than referring to the table? I'm not sure if I'm doing something wrong but I seem to get more accurate answers by just memorizing those numbers.

Here's an example of a problem I just did:

The test scores on the quantitative portion of the SAT are normally distributed with a mean score of 570 and SD of 70. Using the empirical rule, approximately what percent of the scores are more than 710?

I used the formula: z = x-mu/sigma

= (710 - 570)/70 = 2

If I use the method of memorizing the numbers and drawing it out using them, I get 2.5% which is the answer the CD for my book has.

(my work = p (z > 2 ) = 0.5 - 0.34 - 0.135 = .025 = 2.5%

If I use the table, it turns out like this:

P (z > 2) = 0.5 - 0.4772 = 0.0228 = 2.3%?

The CD program marks 2.3% as incorrect. Am I doing something wrong? Or are both answers acceptable?

For this z-score; 2.28% is correct and 2.5% is wrong, but your question
says "using the empirical rule", and you need to look see what that is.

It may well be that you are told that the empirical rule is that about 97.5% of the
area under the normal distribution is to the right of z=2, or that about 95% is
within 2 SDs of the mean.

RonL

Oh, sorry, I meant the CD says 2.5% is the correct answer. If I put in 2.3%, it says it's incorrect. I guess I should just rely on the table.

As for the empirical rule, it says: This rule provides the procedure for computing normal probabilities associated with only whole number multiples of the standard deviation (sigma), that is, within 1, 2 or 3 standard deviations of the mean.

I'm not sure what that means. :x