The z transform for the normal distribution is writtenThe normal distribution tables are used as below:
a)Find a value ofusing 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 ofsuch 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 treatand
in the same way and
and
in 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 formula
Since we are assuming here that we have a continuous distribution,
Sometimes you have both instance above simultaneously. So have to findand 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 findsuch that
use
then use the tables to find
and then use the
transform to find
If a probabilityis less than 0.5, find
and use the
value corresponding to this.