## Negative z Values and Points of Confusion

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

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

b)Given a value for a probability, such that look up a value of in the normal distribution tables corresponding to this given value, The corresponding value of may then be worked out using the equation for given 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 2.Find 3.Find values of such that or 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 treat and in the same way and and in the same way.

If you have to find a probability corresponding to a negative value of Ignoring 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 find use the formula Since we are assuming here that we have a continuous distribution, Sometimes you have both instance above simultaneously. So have to find and the value of corresponding to this value of is negative. Be methodical: Use Work out using the equation above. Ignore the minus sign and find the probability from the tables. Find to find and take this answer from 1 to give It is best to be methodical like this in order to get used to the rules.

To find such that use then use the tables to find and then use the transform to find If a probability is less than 0.5, find and use the value corresponding to this.