Examples
Example 1
Determine the area under a normal curve to the left of a z-score of -2.45.
The z-score table lists areas under the normal curve to the left of a given z-score. Select the table with the negative z-scores. To find the area to the left of -2.45, find the cell that corresponds to -2.4 in the left column and 0.05 in the top row.
The table shows 0.0071, so the area to the left of a z-score of -2.45 is 0.0071. This means that 0.71% of the data will have a z-score below -2.45.
(Note that the diagram below has an error: -0.0071 should read 0.0071.)
Example 2
Determine the probability that a value from a normally distributed data set will have a z-score greater than 0.94.
The z-score table lists areas under the normal curve to the left of a given z-score. Select the table with the negative z-scores. To find the area to the left of -2.45, find the cell that corresponds to -2.4 in the left column and 0.05 in the top row.
The table shows that the area to the left of 0.94 is 0.8264.
The total area under the normal curve is 1, so the area to the right of 0.94 must be 1 - 0.8264 = 0.1736 .
The probability that a value from a normally distributed data set will have a z-score greater than 0.94 is 0.1736 or 17.36%.
Example 3
Determine the z-score above which 73% of data lies.
If 73% of data lies above the z-score, then 27% lies below that z-score.
Find the value closest to 0.27 on the inside of one of the z-score tables to determine the z-score.
The z-score is -0.61.
Because the tables only work with z-scores rounded to the nearest hundredth, these tables are somewhat limiting. In the previous example, an exact area of 27%, or 0.27, did not exist in the table and as such the value closest to 0.27 had to suffice.