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Question: The inspection division of the Lee County Weights and Measures Department wants to estimate the actual amount of soft drink in 2-liter bottles at the local bottling plant of a large nationally known soft-drink company. The bottling plant has informed the inspection division that the population standard deviation for 2-liter bottles is 0.05 liter. A random sample of 100 2-liter bottles at this bottling plant indicates a sample mean of 1.99 liters.

a. Construct a 95% confidence interval estimate of the population mean amount of soft drink in each bottle.

b. Must you assume that the population of soft-drink fill is normally distributed? Explain.

c. Explain why a value of 2.02 liters for a single bottle is not unusual, even though it is outside the confidence interval you calculated.

d. Suppose that the sample mean is 1.97 liters. What is your answer to (a)?

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