SOLUTION: The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable. a) Where should the mean be set to e

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Question 352363: The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable. a) Where should the mean be set to ensure a 95 percent probability that a half liter bottle will not be underfilled? b) A 99 percent probability? c) A 99.9 percent probability? Explain.

Answer by stanbon(75887) (Show Source):
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The amount of fill in a half liter soft drink bottle is normally distributed. The process has a std. deviation of 5 ml. The mean is adjustable.
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a) Where should the mean be set to ensure a 95 percent probability that a half liter bottle will not be underfilled?
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A value that is 1.645 std below the mean will have 95% of the data above it.
1.645*5ml = 8.2243ml
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1/2 liter = 500 ml
500-8.2243 = 491.78ml
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Set the mean at 491.78ml
b) A 99 percent probability?
Same as above but use z value of 2.326. That z will have 99% above it.

c) A 99.9 percent probability? Explain.
Same as above but use z value of 3.09. That will have 99.9% above it.
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Cheers,
Stan H.