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?

Question

anonymous · Answer

I need to use the empyrical rule

tkhunny · Answer

(22500-30000)/2500
(37500-30000)/2500

What are these and what do these values tell us?

anonymous · Answer

Um they tell us the mileage of the tire?

anonymous · Answer

or they tell us the dev

tkhunny · Answer

z-scores, standard deviations.  What are the values?  Do the calculations

anonymous · Answer

-3 and 3

tkhunny · Answer

That's it.  And what does the Empirical Rule say about that -- 3 standard deviations each way?

anonymous · Answer

do we place the percentages?

anonymous · Answer

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 · Answer

So how do we place this in this problem could you give me an example?

tkhunny · Answer

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 · Answer

So the answer to my question is 99.7% right