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Standard Deviation Word Problem

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data
    It has been projected that the average and standard deviation of the amount of time spent online using the Internet are, respectively, 14 and 17 hours per person per year (approximately normally distributed). What value is exactly 1 standard deviation below the mean?


    2. Relevant equations
    Emiprical Rule
    [tex]\mu \pm \sigma[/tex] contains approximately 68% of the measurements.
    [tex]\mu \pm 2\sigma[/tex] contains approximately 95% of the measurements.
    [tex]\mu \pm 3\sigma[/tex] contains approximately almost all of the measurements.

    3. The attempt at a solution
    In similar problems, the mean is the larger number in the problem, so solving the problem is a simple matter of subtracting the standard deviation from the mean to find out the percentage of population.

    In this case though, the standard deviation (17) is greater than the mean(14)? If I solve this like I do normal problems, this would leave me with a negative value for time spent on the Internet.

    Is this an error in the text book or is there something I'm missing here?
     
  2. jcsd
  3. Sep 21, 2009 #2

    jambaugh

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    Science Advisor
    Gold Member

    My guess is that the problem is meant to emphasize the shortcomings of assuming a normal distribution, e.g. the normal distribution spans the entire real line while examples may have a restricted domain, as in this case only positive reals.
     
  4. Sep 21, 2009 #3
    Thanks
     
  5. Sep 21, 2009 #4

    statdad

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    Homework Helper

    It should be used to reinforce the idea that assuming things are normally distributed isn't always justified: the actual question as you describe it shows that the times can't be normal, for the reason you point out.
     
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