Question: A bottling company sets a machine to fill 12 ounces of a soft drink in every bottle. A

State inspector, in looking out for customers, selects a random sample of 49 bottles

once a week. If the mean of the sample is less than 11.98 ounces, the company is

given a $1000 fine. Assume that the population standard deviation is 0.07 ounces.

1. Find the mean and standard deviation of the distribution of the mean of the samples selected by the inspector.
2. What is the shape of the distribution of \(\text{\bar{X}}\). Explain.
3. Find the probability that the mean of an inspector’s sample is less than 11.98 ounces.
4. Find the probability that a bottle selected at random has less than 11.98 ounces of the soft drink.

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