math statistics

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The average price of a gallon of unleaded regular gasoline was reported to be $2.34 in northern Kentucky (The Cincinnati Enquirer, January 21, 2006). Use this price as the population mean, and assume the population standard deviation is $.20.

1. What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean (to 4 decimals)?


2. What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean (to 4 decimals)?


3. What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean (to 4 decimals)?


4. Calculate the sample size necessary to guarantee at least .95 probability that the sample mean is within $.03 of the population mean (0 decimals).

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