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Chebyshev's Theorem Limit Question-Value Greater than 1

  1. Jun 6, 2009 #1
    1. The problem statement, all variables and given/known data

    According to Nielsen Media Research, kids ages 12-17 watch an average of 3 hours of tv per day. Suppose that the standard deviation is 1 hour and that the distribution of time spent watching tv has a bell-shaped distribution.

    a) what percentage of kids aged 12-17 watch tv between 2 and 3 hours per day?


    2. Relevant equations

    1-1/z^2

    3. The attempt at a solution

    The standard deviation of 2 hours is 1, from the mean. But the value of z has to be greater than 1. With a question that has a range in it, usually means both sides will have a standard deviation from the mean. But one side is 1 and the other is the same as the mean.

    So we only have one side, and I divided 1 in half to get .5 and plugged it into the formula.

    1-1/.5^2

    1-1/.25

    1-4

    -3

    The answer is 34%.

    I know I'm missing a step but I don't know what step. The formula is pretty straight forward and I get it, but this problem is really messing me up.
     
  2. jcsd
  3. Jun 6, 2009 #2

    diazona

    User Avatar
    Homework Helper

    Chebyshev's inequality only makes a general statement about any probability distribution. So for example, if you plug in z = 1, you get 1-1/z^2 = 0, which means that no less than 0 of the values are more than 1 standard deviation away from the mean. But in this case, you know that the distribution is normal (a bell curve), so you can get a more precise answer, which is going to be the 34%.

    As for how to get that 34%... look it up maybe? Or if you know the formula for the cumulative normal distribution (the error function), you can use that.
     
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