Guys, Thanks for your efforts and time explaining this, it now makes sense (I think). I can see that I was assuming the empirical rule is an exact value when it's really only an estimate. So the greater the population the more precise the empirical rule is...also maybe the question which I used as an example (taken from an assignment mind you) should read something like..." if the grades have a normal mound shape distribution..." Pondering a little... I can see now there are mound shaped distributions which skew to the left and right etc...so the question does seem a little vague..
Hope these opinions make sense....I'm only new at this! Thanks again for the help and prompt responses. p.s Promise not to post twice...Stan, u sure whip the first timers into place quick smart! Cheers ~Mel "Stan Brown" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > In article <[EMAIL PROTECTED]> in > sci.stat.edu, Mel <[EMAIL PROTECTED]> wrote: > > >Anyones help with the below would be appreciated. > > I'll help, if you'll promise not to post the same article multiple > times in future. This is Usenet, and it may take quite some time > even for your own article to show up on your own server, let alone > any replies. > > >"500 students took an exam, the mean was 69 and the standard deviation was > >7. if the grades have a mound shape distribution, how many students > >recieved a grade of more than 83" > > [summary of what Mel said: > z = 2; 68-95-99.7 rule says 95% of data occur -2 < z < 2, therefore > 2.5% of data are above z = 2. 2.5% of 500 is 12.5 students] > > Your calculation is correct. I congratulate you for going further > and actually thinking about what this _means_! Perhaps I can help > with the interpretation. > > >I have no idea if the above is correct ( I don't think it is), but it > >dosen't seem logical that 12.5 students recieved more than 83, as I've never > >encountered a half person before! I think I've missed something.. > > The empirical rule tells you that _about_ 2.5% of the data will lie > above z = 2 in a normal distribution, not that _exactly_ 2.5% will > lie above. The smaller the population, the less closely it will > approach an ideal normal distribution and therefore the less good > that empirical rule will be. For 500 students the approximation > should not be too bad, _if_ the underlying distribution is > normal.(*) So your calculation correctly tells you that _about_ 12.5 > students will have scores over 83. You would simply state this as > about 12 or 13 students. > > (*) I'm a little uneasy about that "mound shape distribution" in the > problem statement. I hope you understand, Mel, that the empirical > rule does not apply to every mound-shaped distribution but only to > normal distributions. Other mound-shaped distributions will differ > from the empirical rule to a greater or lesser extent. > > -- > Stan Brown, Oak Road Systems, Cortland County, New York, USA > http://OakRoadSystems.com/ > It's not necessary to send me a copy of anything you post > publicly, but if you do please identify it explicitly to avoid > confusion. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
