Pittsburgh Business Daily

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?

Public Comments

1. The formula is discussed on the Wikipedia page: http://en.wikipedia.org/wiki/Normal_distribution
2. Do you know integral calculus? You plug into your calculator, y = e^(−z²) / √(π) Then you integrate that with respect to z, from −∞ (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<z) = ∫{−∞→z} e^(−Z²) / √(π) dZ The compliment of it is the area to the right. P(Z>z) = 1 − P(Z<z) P(Z>z) = ∫{z→∞} e^(−Z²) / √(π) 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^(−x²) / √(π) 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.