What is the formula for finding the values on a z-score table?

Many places tend to direct me to probability distribution tables when I try to find the formula for calculating the actual values on the table. For example:

mean = 100

Standard dev = 15

Raw score = 120

z score = 1.33



On a table, this is no problem to find, but in a scenario when I do not have a table, how do I calculate to find the percentile or (whatever the value of .9082 is called) on the table?What is the formula for finding the values on a z-score table?
Do you know integral calculus?



You plug into your calculator, y = e^(鈭抸虏) / 鈭?蟺)



Then you integrate that with respect to z, from 鈭掆垶 (as the lower limit of integration) to the z-score you are checking (as the upper limit of integration).



This gives you the area under the standardized bell curve on the left side of a particular z-score.



So, the probability that a random variable Z will be less than a given z-score, z, is:

P(Z%26lt;z) = 鈭珄鈭掆垶鈫抸} e^(鈭抁虏) / 鈭?蟺) dZ



The compliment of it is the area to the right.

P(Z%26gt;z) = 1 鈭?P(Z%26lt;z)

P(Z%26gt;z) = 鈭珄z鈫掆垶} e^(鈭抁虏) / 鈭?蟺) dZ



If you havent taken integral calculus then its not expected for you to know where/how the tables are derived. And I would expect my answer to be over your head.



Most calculators have statistics commands programmed in, anyway. So instead of having to integrate mathematically, you could just input your z-scores.



Just know that the bell curve is drawn

y = e^(鈭抶虏) / 鈭?蟺)

Pick some value along the x-axis and call it a z-score. Draw a vertical line from the x-axis all the way up to the curve. Everything to the left of this line/z-score and above the x-axis and below the curve... that whole area... is what you get out of a z-score table.What is the formula for finding the values on a z-score table?
The formula is discussed on the Wikipedia page: http://en.wikipedia.org/wiki/Normal_dist鈥?/a>