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

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

a)Find a value ofusinga given value ofusingthe above formula, then going to the normal distribution tables tolook up a probability using this calculated value ofor

b)Given a value for a probability,suchthatlookup a value ofinthe normal distribution tables corresponding to this given value,Thecorresponding value ofmay then be worked out using the equation forgivenabove.

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 ofsuchthator

4.Deal with a probability less than 0.5.

I will assume throughout here that we have a continuous normaldistribution. This means we can treatandinthe same way andandinthe 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 findusethe formulaSincewe are assuming here that we have a continuous distribution,

Sometimes you have both instance above simultaneously. So haveto findandthe value ofcorrespondingto this value ofisnegative. Be methodical: UseWork outusingthe equation above. Ignore the minus sign and find theprobabilityfromthe tables. Findtofindandtake this answer from 1 to giveItis best to be methodical like this in order to get used to the rules.

To findsuchthatusethenuse the tables to findandthen use thetransformto find

If a probabilityisless than 0.5, findanduse thevaluecorresponding to this.