The amount of fill in a half-liter (500 ml) soft drink bottle is normally distri

Question

The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 2.0 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? (Round your answer to 2 decimal places.)  

Mean             ml

(b) Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)  

Mean             ml

(c) Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.)  

Mean             ml

Explanation / Answer

Q1) At 95% below data , critical value is 1.645

Set the mean at = 500-1.645*2

Set the mean at = 496.71 ml

b) At 99% below data , critical value is 2.3263

Set the mean at = 500-2.3263*2

Set the mean at = 495.35 ml

c) At 99.9% below data , critical value is 3.0902

Set the mean at = 500-3.0902*2

Set the mean at = 493.82 ml

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