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?