The z transform for the normal distribution is writtenThe normal distribution tables are used as below:
a)Find a value ofusing a given value ofusing the above formula, then going to the normal distribution tables to look up a probability using this calculated value ofor
b)Given a value for a probability,such thatlook up a value ofin the normal distribution tables corresponding to this given value,The corresponding value of may then be worked out using the equation forgiven above.
Because of the way normal tables are usually presented there is often a lot of confusion over how to:
1.Find the probability corresponding to a negative value of
3.Find values ofsuch thator
4.Deal with a probability less than 0.5.
I will assume throughout here that we have a continuous normal distribution. This means we can treatandin the same way andandin the same way.
If you have to find a probability corresponding to a negative value ofIgnoring the negative, go to the tables to find the probability p corresponding to that positive value of Having done this, find
If you have to finduse the formulaSince we are assuming here that we have a continuous distribution,
Sometimes you have both instance above simultaneously. So have to findand the value ofcorresponding to this value ofis negative. Be methodical: Use Work outusing the equation above. Ignore the minus sign and find the probabilityfrom the tables. Findto findand take this answer from 1 to giveIt is best to be methodical like this in order to get used to the rules.
To findsuch thatusethen use the tables to findand then use thetransform to find
If a probabilityis less than 0.5, findand use thevalue corresponding to this.