How to Deal With Negative z Values When Using the Normal Distribution

The z transform for the normal distribution is written Thenormal distribution tables are used as below:

a)Find a value of usinga given value of usingthe above formula, then going to the normal distribution tables tolook up a probability using this calculated value of or

b)Given a value for a probability, suchthat lookup a value of inthe normal distribution tables corresponding to this given value, Thecorresponding value of may then be worked out using the equation for givenabove.

Because of the way normal tables are usually presented there isoften a lot of confusion over how to:

1.Find the probability corresponding to a negative value of 2.Find 3.Find values of suchthat or 4.Deal with a probability less than 0.5.

I will assume throughout here that we have a continuous normaldistribution. This means we can treat and inthe same way and and inthe same way.

Ignoringthe negative, go to the tables to find the probability pcorresponding to that positive value of Having done this, find If you have to find usethe formula Sincewe are assuming here that we have a continuous distribution, Sometimes you have both instance above simultaneously. So haveto find andthe value of correspondingto this value of isnegative. Be methodical: Use Work out usingthe equation above. Ignore the minus sign and find theprobability fromthe tables. Find tofind andtake this answer from 1 to give Itis best to be methodical like this in order to get used to the rules.

To find suchthat use thenuse the tables to find andthen use the transformto find If a probability isless than 0.5, find anduse the valuecorresponding to this. 