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Studies shown that gasoline use for compact cars sold in the U.S. is normally distributed, with a mean of 25.5 mpg and standard deviation of 4.5 mpg. Find the range of mileage for the middle 60% of compact cars.

I believe that you subtract x from 25.5 then divide by 4.5. find x and then place it into 25.5+(x)(4.5). but I do not know what to do with the 60%

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  • $\begingroup$ If you look at a standard normal table, you will see that $60\%$ of the probability lies between $z=-0.84$ and $z=0.84$. So for the cars the range will be $25.5\pm (4.5)(0.84)$. $\endgroup$ – André Nicolas Nov 18 '14 at 15:17
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Consider:

Experiment: Randomly select one compact car

Random Variable $MPG$: $M$iles $P$er $G$allon

Possible Values $mpg$: [$0$ mpg, $600$ mpg]

Determine $mpg_1$ and $mpg_2$: $P$($mpg_1$ $\le$ $MPG$ $\le$ $mpg_2$) $= 0.60$.

enter image description here

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The mean +/- 1σ is about 68% of the total. So you want less than +/- 1σ. Look here: http://upload.wikimedia.org/wikipedia/commons/7/75/Standard_score_and_prediction_interval.png If you read the chart to get 60%, you'll see you need about +/- 0.84σ.

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