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

[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 🙂

 

[LetsGo2DSchool]

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%

 

[hazel25]

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

 

[LetsGo2DSchool]

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

 

[hazel25]

ok gotcha, thanks for explaining this!

 

[toothhornet88]

Im a visual person so here is my help. This can give you a picture of what the other posters stated

 

[Plethora330]

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%

bahaha, man you are from NY Thanks for the explanation