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 4.5 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.)  

(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.)  

(c) Where should the mean be set to ensure a 99.0 percent probability that a half-liter bottle will not be underfilled?

Explanation / Answer

a) Let the mean be set at M.

For 90% probability of not uunderfilling, z = 1.28

Hence,

Mean = 500 + 1.28*4.5 = 505.76 ml

b) Let the mean be set at M.

For 95% probability of not uunderfilling, z = 1.645

Hence,

Mean = 500 + 1.645*4.5 = 507.40 ml

c) Let the mean be set at M.

For 99% probability of not uunderfilling, z = 2.33

Hence,

Mean = 500 + 2.33*4.5 = 510.49 ml

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