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# Central limit theorem/sampling distribution of a sample mean

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A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters. In fact, the contents vary according to a normal distribution with mean=298 ml and standard deviation=3 ml.
a)What is the probability that an individual bottle contains less than 295 ml?
b)What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml?

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#### Solution Summary

The solution discusses a bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters. In fact, the contents vary according to a normal distribution with mean=298 ml and standard deviation=3 ml.
a)What is the probability that an individual bottle contains less than 295 ml?
b)What is the probability that the mean contents of the bottles in a six-pack is less than 295 ml?

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