anonymous
  • anonymous
The mean lifetime of a certain tire is 30,000 miles and the standard deviation is 2500 miles. If we assume the mileages are normally distributed, approximately what percentage of all such tires will last between 22,500 and 37,500 miles?
Statistics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I need to use the empyrical rule
tkhunny
  • tkhunny
(22500-30000)/2500 (37500-30000)/2500 What are these and what do these values tell us?
anonymous
  • anonymous
Um they tell us the mileage of the tire?

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anonymous
  • anonymous
or they tell us the dev
tkhunny
  • tkhunny
z-scores, standard deviations. What are the values? Do the calculations
anonymous
  • anonymous
-3 and 3
tkhunny
  • tkhunny
That's it. And what does the Empirical Rule say about that -- 3 standard deviations each way?
anonymous
  • anonymous
do we place the percentages?
anonymous
  • anonymous
The empirical rule says that if you go 1 standard deviation out from the mean that you will capture 68 % of your data, Go out one more stan dev (thats 2 so far) and you will capture 95% of your data, go out one more (thats 3 so far) and you will capture 99.7% of your data.
anonymous
  • anonymous
So how do we place this in this problem could you give me an example?
tkhunny
  • tkhunny
It's not a matter of placing or calculating. This is the point of the "Empirical Rule". You just read off the result. +/- 1 Standard Deviation is 68% +/- 2 Standard Deviations is 95% +/- 3 Standard Deviations is 99.7% In this case, pick the third one. Done.
anonymous
  • anonymous
So the answer to my question is 99.7% right

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