Chapter Exercise 7-92 The amount of fill in a half-liter (500 ml) soft drink bot

Question

Chapter Exercise 7-92 The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 5.5 ml. The mean is adjustable (a) Where should the mean be set to ensure a 90 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.) Mean (b) 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 (c) Where should the mean be set to ensure a 99.0 percent probability that a half-liter bottle will not be underfilled? (Round your answer to 2 decimal places.) Mean ml ml ml

Explanation / Answer

a)

A value that is 1.28 std below the mean will have 90% of the data above it.

1.28 * 5.5ml = 7.04ml
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1/2 liter = 500 ml

500 - 7.04 = 492.96ml

b)

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

1.645 * 5.5ml = 9.05ml
-----
1/2 liter = 500 ml

500 - 9.05 = 490.95 ml

c)

A value that is 3.09 std below the mean will have 99% of the data above it.

3.09 * 5.5ml = 16.995ml
-----
1/2 liter = 500 ml

500 - 16.995 = 483.005 ml

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