Question

hello i wanted to know the process for finding the z value when area is given and also vice versa using spss software

Answer 1

To find the z value or x value when we know the area to the left , we have to use function IDF.NORMAL( area to the left , mean , sd )

To find the area or % to the left of z or x value , we have to use function CDF.NORMAL( x , mean , sd )

For example 1 :

If we have mean = 100 , sd = 15 and we have to find x such that area to the left of x is 0.95

So first in "data view " enter the 100 and 15 in the 1st and 2nd column and then go to "variable view"

and name the column mean and sd respectively.

So you get column names mean and sd in data view with the entered numbers 100 and 15 respectively.

Then go to "Transform" menu ---> click on Compute variable.

Then compute variable window will be appeared :

Then in function group: , select inverse DF and then in Function and special variables: select and click on Idf.Normal

IDF.NORMAL will be appeared in Numeric expression window

Always enter the value in manner IDF.NORMAL( area less than x , mean ,sd )

So expression will be IDF.NORMAL(0.95 ,100 ,15 ) as shown in the above picture.

In target variable window plug x and click on OK tab , the answer will be appeared on the "data view" tab in the the column x

You can get the value of x rounded to specified decimal places by making changes in "variable view" for x variable.

Note : the example is given to find x value for given mean and sd value , if you want to find z value for given (left tail ) area , just use mean =0 and sd = 1

Example 2 :

Now to find area to the left or percentile for given value of x or z , we use function CDF.NORMAL( x , mean , sd )

Mean = 100 , sd = 15 and x = 125

We have to find P( x <=125)

Then go to "Transform" menu ---> click on Compute variable.

Then compute variable window will be appeared :

First clear or delele if any previous expression in "numeric expression" window.

Then in function group: , select CDF and Noncentral CDF function and then in Function and special variables: select and click on Cdf.Normal

CDF.NORMAL( ) function will be appeared in Numeric Expression window.

Always enter the values in manner of CDF.NORMAL(x, mean ,sd )

So expression will be CDF.NORMAL(125 ,100 ,15 ) as shown in the above picture.

In target variable window enter P and click on OK tab , the answer will be appeared on the "data view" tab in the the column P

You can get the value of P rounded to specified decimal places by making changes in "variable view" for x variable. ( I have changed to 4 decimals instead of 2 )

Note : the example is given to find area below x value for given mean and sd value , if you want to find area below given z value , just use mean =0 and sd = 1