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Finding Cumulative Proportions of Normal Distributions
Excel and similar spreadsheet software:
Use the formula: =normdist(x, µ, σ, TRUE), where
• x = cut-off value
• µ = mean of Normal distribution
• σ = standard deviation of Normal distribution
For example, if adults’ IQ scores follow a Normal distribution with mean 100 and standard
deviation 15, then the proportion of adults who score less than 110 is given by
=normdist(110, 100, 15, TRUE)
To compute the cut-off value for a given percentage, use the formula:
=norminv(proportion, µ, σ).
For example, =norminv(.8, 100, 15) gives the score below which 80% of adults rank. So from
the calculation shown below, 80% of adults score below 112.6243.
TI-83 and similar calculators: