```Date: Fri, 27 Apr 2007 16:53:32 -0400 Reply-To: "Wainwright, Andrea" Sender: "SAS(r) Discussion" From: "Wainwright, Andrea" Subject: Re: Central Limit Theorem Comments: To: Peter Flom In-Reply-To: A<13044437.1177706923759.JavaMail.root@mswamui-blood.atl.sa.earthlink.net> Content-Type: text/plain; charset="us-ascii" In reading the original I had the same response you did. The distribution of the mean from multiple samples will be approximately normal, but any given sample can't be assured to be normally distributed. -----Original Message----- From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Peter Flom Sent: Friday, April 27, 2007 4:49 PM To: SAS-L@LISTSERV.UGA.EDU Subject: Central Limit Theorem I am reviewing and editing a statistics book. In it, they have the following statement re the central limit theorem "Regardless of the shape of the population, if a sufficiently large random sample of size n is taken from the population, then the sample is approximately normally distributed, with mean mu sub xbar and standard deviation sigma/sqrt(n)" ???? This seems completely wrong! The CLM is not about ONE sample, but about MANY samples. That is, it should be "Regardless of the shape of the population, if a sufficiently large NUMBER of samples of a particular size is taken, then the distribution of the mean of the SAMPLES approaches normal as the NUMBER of samples approaches infinity" I googled a bit, and did not find a really good clear statement of this - the book is intended for HS students. Anyone got any suggestions? Am I all wrong? Is the author all wrong? Are we BOTH wrong? Happy weekend! Peter The information contained in this e-mail is confidential and/or proprietary to Capital One and/or its affiliates. The information transmitted herewith is intended only for use by the individual or entity to which it is addressed. If the reader of this message is not the intended recipient, you are hereby notified that any review, retransmission, dissemination, distribution, copying or other use of, or taking of any action in reliance upon this information is strictly prohibited. If you have received this communication in error, please contact the sender and delete the material from your computer. ```

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