z score help?

[mea]

I did z score stuff in my last stats course but can't seem to remember it all. I have a group of 33 standard scores and I want to find out what percentage fall below 1. How do I figure this out. I don't want anyone to give me the answer, just please walk me through the process.
Also, how do I then calculate the cumulative percentage of standard scores less than 1?
Thanks.

[Mean Joe]

I did z score stuff in my last stats course but can't seem to remember it all. I have a group of 33 standard scores and I want to find out what percentage fall below 1. How do I figure this out. I don't want anyone to give me the answer, just please walk me through the process.
Also, how do I then calculate the cumulative percentage of standard scores less than 1?
Thanks.

To change your standard scores into z-scores, you'll need to find two things:
1) the sample mean of the 33 scores
2) the sample standard deviation of the 33 scores.

Then you convert each standard score, 1 by 1: (standard score - sample mean) / (sample standard deviation).

In theory, 15.87% of standard scores (from a normal distribution) would have a z-score greater than 1. So that cumulatively 84.13% have a standard score less than 1. Another 15.87% would have a z-score less than -1. So 68.26% would have a z-score between -1 and 1 (i.e. absolute value less than 1). I got these numbers from looking at a standard normal table.

You have to read the "fine print" on the table, to see what probabilities are given in the table, e.g. some tables give the "area under the curve to the right of z", others give the "area under the curve to the left of z", and there's other possibilities.