Stats problem -- suggestions..

Discussion in 'Off-Topic Discussions' started by Mr. Engineer, Apr 21, 2005.

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  1. Mr. Engineer

    Mr. Engineer member

    OK – OK – so I am the very first to admit, even as a Staff Engineer, I am crummy at math. I am working on a Statistics/Probability question and would like some feedback from some of the math guru’s in the audience.

    Here is the question

    I have a population that makes an average of $24.07 per hour
    The standard deviation is $4.80
    The sample size is 120 individuals

    What is the possiblility that the sample mean will be within 50 cents of the population mean?

    I figured that the range is $23.57 to $24.57

    23.57 – 24.47 / 4.80 = -0.2083 or -20.83% chance that the sample mean will be within 50 cents of the population mean.

    This looks too easy – am I doing something wrong or leaving something out?
     
  2. Myoptimism

    Myoptimism New Member

    Okay.
    I'm not any kind of math guru, but this is how I would approach it. You need to find the t value for both your upper $.50 limit ($24.57) and your lower limit ($23.57).
    You can find a "very close" (because of the relatively large n) z value(s) to substitute for the t value(s) by subtracting the average from you limit(s), and then dividing by the standard deviation. Then plug the numbers into your z table, subtract the lower from the higher, and there is a very close approximation of the probability.
    Or, you could use excel (or a stats program) to find out the exact probability.
    I think it should be somewhere around 8%.

    Tony

    P.S. I sincerely hope this isn't misleading, but if it is, I hope someone corrects me. Thanks.
     
    Last edited by a moderator: Apr 21, 2005
  3. Ian Anderson

    Ian Anderson Active Member

    Once N > 30 then the sample mean is usually a good estimate of the population mean.

    Using the Central Limit Theorem

    Std error = (std Dev)/(N^0.5) = .4382

    Z1 = (23.57 - 24.07)/.4382 = -1.141
    Z2 = (24.57 – 24.07)/.4382 = +1.141

    Probability equals the area under the normal curve = .8729 - .1271 = .7458 (74.58%)

    Ref: Walpole & Meyers. Probability and Statistics for Engineers and Scientists. Macmillan. Fourth Ed. (Chapter 6.8). (My MSQA Statistics textbook)
     
    Last edited by a moderator: Apr 22, 2005
  4. Myoptimism

    Myoptimism New Member

    You're right, Ian. I misread the problem, and was looking for the percentage of the sample population within $.50 either way.
    Sorry. :(

    Tony
     
  5. Bill Hurd

    Bill Hurd New Member

    looks to me like it is 11.3%, but I defer to others

    BH
     
  6. Ian Anderson

    Ian Anderson Active Member

    I just returned from vacation. Did you find the correct answer to your statistic problem?
     
  7. DesElms

    DesElms New Member

    I think Chip should start a "Help With Homework" category.

    ;)
     
  8. Mr. Engineer

    Mr. Engineer member

    Actually Ian's answer was correct. I went through the problem several times before coming up with the right answer -- and Ian confirmed it.

    Thanks for all of the help!
    W.
     

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