Please round answer to 2 decimal places: The amount of fill in a half-liter (500

Question

Please round answer to 2 decimal places:

The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 2.5 ml. The mean is adjustable. Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be undefiled? (Round your answer to 2 decimal places.) Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be undrilled? (Round your answer to 2 decimal places.) Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be undefiled? (Round your answer to 2 decimal places.)

Explanation / Answer

(a) A value that is 1.645 std below the mean will have 95% of the data above it

         1.645*2.5ml=4.1125ml

Half liter =500ml

500-4.1125=495.88 ml

   495.88 mean be set to ensure a 90 percent probability that a half-liter bottle will not be underfilled.

(b) A value that is 2.326 std below the mean will have 99% of the data above it

      2.326*2.5ml=5.815ml

Half liter =500ml

500-5.815=494.185 ml

494.18 mean be set to ensure a 99percent probability that a half-liter bottle will not be underfilled

(c) A value that is 3.09 std below the mean will have 99.9% of the data above it

     3.09*2.5ml=7.725ml

Half liter =500ml

500-7.725=492.275 ml

492.28 mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled

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