Re: statistics question for a business research course

In article <1125260246.497150.54600@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Randy Poe <poespam-trap@xxxxxxxxx> wrote:
>
>John Smith wrote:
>> You draw a random sample of 300 employee records from the personnel file
>> and find that the average years of service per employee is 6.3, with a
>> standard deviation of 3.0 years. (a) What percentage of the workers would
>> you expect to have more than 9.3 years of service? (b) What percentage
>> would you expect to have more than 5.0 years of service?

>> No other information is given.

>Technically, there is not enough information given to solve
>the problem since they haven't told you what distribution
>the data follows. However, when in doubt a normal (bell
>curve) distribution is usually assumed, and that is probably
>what's intended here.

That may indeed be intended, but a normal distribution is
not very reasonable for this sort of random variable (basically
a lifetime). A Gamma distribution might be more reasonable.
The given data would fit a Gamma distribution with scale
parameter 10/7 and shape parameter 4.41. That would make
the answers to (a) and (b) approximately 15.2% and 62.0%
respectively.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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