This is one of the following eight articles on the normal distribution in Excel
An Important Difference
Between t and Normal
The t-Distribution is a family of distribution curves that are all symmetrical about a mean of zero. Each unique curve of the t-Distribution is completely described and fully differentiated from all other t-Distribution curves by its degrees of freedom, which is designated by either df or v (Greek letter “nu”). Degrees of freedom is related to sample size by df = n – 1.
The t-Distribution’s PDF formula calculates the PDF at the t Value of point X. The t Value of point X is the number of standard errors that point X is from the sample mean. When calculating the t-Distribution’s PDF (or CDF) at point X, the t Value of point X must be computed for that point X. The t Value of point X is the required input of the t-Distribution’s PDF (and CDF) formula.
The t Value of point X must be determined as follows:
before the t-Distribution’s PDF can be calculated by the following formula:
The Excel formula to calculate the t-Distribution’s PDF is shown here as well.
f(t,v) = T.DIST(t, df, FALSE)
The t Value of the point X must also be calculated before calculating the t-Distribution’s CDF, which can be found with the following Excel formula:
F(t,v) = T.DIST(t, df, TRUE)
The normal distribution is also a family of distribution curves. Each distribution curve is fully described and completely differentiated from all other normal curves by only two parameters: its mean, μ, and standard deviation, σ.
The normal distribution’s PDF at point X is calculated directly by using point X as one of the inputs of the normal distribution’s PDF formula as follows:
The Excel formula to calculate the normal distribution’s PDF is shown here as well.
f(X,μ,σ) = NORM.DIST(X, μ, σ, FALSE)
The t-Distribution requires that point X be converted to a t Value before calculating the PDF or CDF at point X. The normal distribution does not require such a conversion because point X is one of the inputs to and part of its PFD and CDF formulas.
The normal distribution’s CDF formula in Excel is as follows:
F(X,μ,σ) = NORM.DIST(X, μ, σ, TRUE)
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