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A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.4 ounces. For the questions that follow, suppose that the company is telling the truth.
(A) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, do it. If not, explain why you cannot.
(B) A quality control inspector measures the contents of an SRS of 50 cans of the company's soda and calculates the sample mean x . Calculate the mean and standard deviation of the sampling distribution of x for samples of size n = 50. Interpret the standard deviation.
(C) What is the shape of the distribution described in part (B)? Justify your answer.
(D) The inspector in part (B) obtains a sample mean of x = 11.9 ounces. Calculate the probability that a random sample of 50 cans produces a sample mean amount of 11.9 ounces or less.
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