Saturday, March 19, 2011

Using the Standard Normal Table to Calculate Probability

You may be familiar with the standard normal distribution and how it can be used to make probability interpretations by looking up values from the standard normal table  that correspond to specific values of z. These values from the table represent the area under the standard normal curve, and have a probability interpretation.

There are 3 instances in which you may be looking at z-values. 1) when z is positive, 2) when z is negative, and 3) when you will be looking at ranges between 2 values of z (which could be positive or negative) Below I outline these instances and the rules you will need to know to correctly use the z-table to calculate probabilities.

z = (x-μ)/σ

1) If z is positive:

a) the probability of observing a lower value of z is the area to the left of z and is the value taken directly from the standard normal table.
b) The probability of a larger value of z is the area to the right of z and = 1-(value from the table)

2) If Z is negative:

a) The probability of a lower z is the area to the left of z and  = 1-(value from table)
b) The probability of a higher value of z is the area to the right of z and = the value directly from the table.

3) The probability of getting a value between -z and z is the area between -z and z. You get this by:

a) calculate the area < - Z= A
b) calculate the area > Z =B
c) calculate 1 - A -B