hi, need help with this problem from the Destroyer

[agogo1212]

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A national survey was conducted on how much dentists charge for a simple tooth extraction . the data was found to be normally distributed with a mean of $320 per extraction and standard deviation of 20 $ . based on this info , apporoximately what percent of the population charge $280 or less for a simple tooth extraction ? I do not understand this, any help will be appreciated

 

[ToofNinja]

68% fall between 1 standard deviation or $300-$340. So $280 and less would be greater than two standard deviations, which is around 0.27%. You just have to memorize the following chart.

 

[the Boss Man]

I think ToofNinja is on the right track. The 68% includes those charging between 300-340 which is 1 SD on each side of the mean. The 95% includes those charging between 280 and 360, 2 SD's on each side of the mean. Meaning that 5% of all dentists charge either less than 280, or more than 360. Since this is normally distributed, and symmetrical on both sides - this is divided in half. 2.5% of all dentists will charge less than $280 for an extraction.

For further understanding, 99.7% of all dentists will charge between 260 and 380 for a tooth extraction, and 0.27% will either charge less than 260 or more than 380 for one.

Explaining the 68-95-99.7 rule for a Normal Distribution

The normal distribution is commonly associated with the 68-95-99.7 rule which you can see in the image above. 68% of the data is within 1…

towardsdatascience.com

Hopefully this is helpful.