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 did not understand math destroyer explanation >>68% , 95% , 99.7 % rule , so If anybody can expain to me this question more cleaier than destroyer i would be more than happy thanks 😍
Normally distributed means bell shaped curve (google it). Essentially it means that the greatest # of items fall at the mean and as you go above and below the mean there are fewer and fewer items. Again, if you have never seen a bell shaped curve, google it for a picture. You'll see what I mean.
Here the mean is $320. This means that this price is charged by the greatest # of dentists overall. Numbers like $330 and $310 are slightly lower in #. Numbers like $340 and $300 are even lower in #. Numbers like $620 and $20 are even lower in #.
The standard deviation shows the spread of the data. The higher the std dev, the more spread out it is. For example if the standard deviation is $100 then you're more likely to see fees in the $400 and $500 range, as well as the $200 and $100 range. If the std dev were $50, we'd be talking about the $375-$450 range and the $200-$275 range. Get it? You'd still see the most fees around the mean but there's a higher # of fees further from the mean if the std dev is larger.
The rule above states that within plus or minus one std dev, you'll find approximately 68% of the data. If the mean is $320 and the std dev is $20, then between $300 and $340 you'll find 68% of the data out there. Remember you are applying this to the population based off of your sample. Given any random fee you find out there, based on the stats you acquired, there's a 68% chance that fee will be between $300 and $340. Get it?
Within + or - 2 std dev is 95% of the data. Here that's $280 and $360. So there's a 95% chance that if you choose a random dentist out there, their fee for this procedure will be between $280 and $360.
Same for + or - 3 std dev. About 99.7% of the data fall within these std devs. In our problem that's $260 and $380.
So basically the vast majority of the fees you'll find out there, based off of the stats in this problem, are between $260 and $380.
You want $280 or less. We've seen this number. It's from + or - 2 std devs. We know that between $280 and $360 you'll find 95% of the population. What's left? 5% of the population. What does this 5% consist of? Everyone ABOVE $360 AND BELOW $280.
What's important about the bell curve is that it is SYMMETRICAL around the mean. So there is the SAME percentage of data above +2 std dev as there is below -2 std dev.
If 5% of the data lies above and below 2 std dev, then 2.5% lies JUST below.
Answer 2.5%.
