Note that a graphics calculator or a computer can also be used to find areas, proportions and probabilities in a normal distribution, rather than the table used here. 3 3 This corresponds to the number in line with \(0.7\) in the left hand column and \(0.05\) in the top row of the table. 2 2 This corresponds to the number \(0.0\) in the left hand column and \(0.03\) in the top row of the table. The first column of the table shows the whole number and tenths place of a z-score. \(\Pr\left(z<0.03\right)=0.512\) or \(51.2\)%. A standard normal distribution table shows a cumulative probability associated with a particular z-score. 1 1 This corresponds to the number in line with \(0.0\) in the left hand column and \(0.00\) in the top row of the table. We can interpret our proportions or percentages as probabilities: Tables come in different layouts, but this table (a portion of the table is shown below) gives the proportion to the left of a chosen z-value of up to 2 decimal places. If we are working with the standard normal distribution we are not restricted to the 68-95-99 rule because tables are available to enable us to find proportions or percentages or probabilities for any value in the distribution.
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