Question 185970: use the "68-95-99.7 rule" to estimate the area lying between values x=1,100 and x=2,600 under the normal curve that has mean 2,100 and standard deviation 500. Use the "Rule" and solve not using a calculator.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! use the "68-95-99.7 rule" to estimate the area lying between values x=1,100 and x=2,600 under the normal curve that has mean 2,100 and standard deviation 500. Use the "Rule" and solve not using a calculator.
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Draw the picture so you can see what is happending.
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1100 is (1100-2600) = -1500, or 1500 to the left of the middle.
That is -1500/500 = -3 , or 3 standard deviations to the left of the mean.
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2600 is (2600-2600) = 0, or 0 from the middle, which is the mean.
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The RULE says 99.7% of the data lies within 3 standard deviations of
the mean. You have half of that or (99.7/2) = 49.85% or 0.4985
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Cheers,
Stan H.
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