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2. You observed the ages of a random sample of 8 men in a bar. The...

2. You observed the ages of a random sample of 8 men in a bar. The average age was 42. It is known that the ages are normally distributed with a standard deviation of 10.

(a) Find a 95% confidence interval for the average age of men in that bar.

(b) Will the 95% confidence interval include approximately 95% of the ages of men in that bar? Explain why or why not.

(c) How many men need to be observed in order for the margin of error of the 95% confidence interval to be at most $5 years?

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