# Question

A machine used for ﬁlling plastic bottles with a soft drink has a known standard deviation of σ = 0.05 liter. The target mean ﬁll volume is µ = 2.0 liters.

(a) Describe the sampling distribution of x̄, the sample mean ﬁll volume, for a random sample of 45 such bottles.

(b) A quality-control manager obtains a random sample of 45 bottles. He will shut down the machine if the sample mean of these 45 bottles is less than 1.98 liters or greater than 2.02 liters. What is the probability that the quality-control manager will shut down the machine even though the machine is correctly calibrated?

(a) Describe the sampling distribution of x̄, the sample mean ﬁll volume, for a random sample of 45 such bottles.

(b) A quality-control manager obtains a random sample of 45 bottles. He will shut down the machine if the sample mean of these 45 bottles is less than 1.98 liters or greater than 2.02 liters. What is the probability that the quality-control manager will shut down the machine even though the machine is correctly calibrated?

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