Percentage Less than a Given ValueDate: 11/22/97 at 00:30:29 From: Joseph Green Subject: Basic descriptive statistics Dear Dr. Math, If some data are normally distributed, and I know the mean and the standard deviation, how do I find out what percentage of the sample is less than (or greater than) a given value? For example, if I'm told that the mean is 12 and the standard deviation is 9, how do I find out what percentage of the sample is less than zero (or greater than 14, etc.)? I thought a t table might be useful for this, but even when I use the row with infinite degrees of freedom (equivalent to z?) I can't figure out how to get an exact answer. (Can't help thinking that I'm overlooking something very simple here.) I'd appreciate any help you can give. Sincerely, Joseph Green Date: 11/22/97 at 06:20:49 From: Doctor Mitteldorf Subject: Re: Basic descriptive statistics Dear Joseph, The answer you're looking for comes from an integral of the normal function y = exp(-x^2/2). The integral is called the error function, erf, and is tabulated in any book of statistics or mathematical tables. But there's no "formula" for the integral. For example, if the mean is 12 and the sd is 9 and you want to find out what percentage of your sample is less than 0, you first calculate that 0 is 1.333 sd's out from the mean, and look up 1.333 in your table. In the table I'm looking at, it says that .4088 is the area between the mean and 1.333 sd's, and I know that the area on each side of the center is exactly .5, so that leaves .0912 as the proportion that is more than 1.333 sd's to the left of the mean. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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