# 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.

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

2. ### LetsGo2DSchool Removed 2+ Year Member

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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%

3. OP

### hazel25

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

4. ### LetsGo2DSchool Removed 2+ Year Member

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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
Last edited: Aug 5, 2011
5. OP

### hazel25

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ok gotcha, thanks for explaining this!

6. ### toothhornet88 7+ Year Member

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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

7. ### Plethora330

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bahaha, man you are from NY Thanks for the explanation

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