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.
.
.
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