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Can somebody explain the Empirical principle : 68%-95%-99.7%?

Discussion in 'DAT Discussions' started by hazel25, Aug 5, 2011.

  1. hazel25

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    destroyer test 4 #21:
    According to a nationwide survey, the cost of a tooth extraction is normally distributed with a mean of $220 and a standard deviation of $30. If a dentist is chosen at random, use the Empirical Rule to determine the probability that he or she charges between $250 and $280 for an extraction.

    answer is 13.5 %

    I have been reading this but doesnt make sense to me, i am not a math person if someone can help id appreciate it :)
     
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  3. LetsGo2DSchool

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    Some douche a long time ago came up with this bell shape distribution curve. What a douche...

    Anyway, the percentages are 68% - 95% - 99.7% and are directly related to the number of standard deviations from the mean.

    So start with the mean $220 and figure out the price points at each standard deviation of $30:

    $160 --- $190 --- $220 --- $250 --- $280

    Using the percentages:

    $160 <---13.5% ---> $190 <---34% ---> $220 mean <--- 34% ---> $250 <--- 13.5% ---> $280

    Thus, the probability of the dentist charging between $250 and $280 is 13.5%
     
  4. hazel25

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    how are you getting the 13.5 % and 34 % in between the amounts?
     
  5. LetsGo2DSchool

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    68% pertains to 68% encompassing the mean which is 34% on each side of the mean.

    $190 <---34% ---> $220 mean <--- 34% ---> $250
    $190 <------------------- 68% ------------------> $250


    95% pertains to 95% encompassing the mean which is 47% on each of the mean, or 13.5% on each side of the 34% number.

    $160 <---13.5% ---> $190 <---34% ---> $220 mean <--- 34% ---> $250 <--- 13.5% ---> $280
    $160 <--------------- 47.5% -------------->$220 mean <--------------- 47.5% ---------------> $280
    $160 <--------------------------------------------- 95% -------------------------------------------> $280
     
    #4 LetsGo2DSchool, Aug 5, 2011
    Last edited: Aug 5, 2011
  6. hazel25

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    ok gotcha, thanks for explaining this!
     
  7. toothhornet88

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    Im a visual person so here is my help. This can give you a picture of what the other posters stated
    [​IMG]
     
  8. Plethora330

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    bahaha, man you are from NY:laugh: Thanks for the explanation
     

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