Question 420520: A machine is used to fill plastic soda bottles. The amount of soda dispensed into each bottle varies slightly. Suppose the amount of soda dispensed into the bottle is normally distributed. If at least 99% of the bottle must have between 585 and 595 milliliters of soda, find the greatest standard deviation, to the nearest hundredth, than can be allowed.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A machine is used to fill plastic soda bottles. The amount of soda dispensed into each bottle varies slightly. Suppose the amount of soda dispensed into the bottle is normally distributed. If at least 99% of the bottles must have between 585 and 595 milliliters of soda, find the greatest standard deviation, to the nearest hundredth, than can be allowed.
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Draw the picture.
The center of the interval [585,595] is 590
That is the mean
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The area to the left of 585 is 0.005
Find the z-value with a left tail of 0.005
invNorm(0.005) = -2.5758
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Find s if x = zs+u
585 = -2.5758s + 590
-2.5758s = -5
s = 1.9411
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Cheers,
Stan H.
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