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Probability of gas prices

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The average price of a gallon of unleaded regular gasoline was reported to be $3.13 in Illinois (http://www.cincygasprices.com).

Use this price as the population mean, and assume the population standard deviation is $.20.

A) What is the probability that the mean price for a sample of 30 service stations is within $.03 of the population mean?
B) What is the probability that the mean price for a sample of 50 service stations is within $.03 of the population mean?
C) What is the probability that the mean price for a sample of 100 service stations is within $.03 of the population mean?
D) Which, if any, of the sample sizes in parts (A), (B), and (C) would your recommend to have at least a .95 probability that the sample mean is within $.03 of the population mean?

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John is considering buying a new pick up truck for his house-cleaning service for middle class customers. The middle class clients seem to be growing even though the economy seems to be not that hot. He is wondering whether he should opt for a sub-compact, or compact or full size pick up. The smaller truck would have better fuel economy, but would sacrifice capacity and durability. A client who works for Big Four Economic Research told him that there is a 30% chance of lower gas prices in this area this year, 20% chance of higher gas prices, and a 50% chance that the gas prices will remain unchanged.

Based on this information and using his girlfriend's financial knowledge, they have developed a decision table that indicates the profit amounts at the end of the year for each combination of truck and gas prices. Help decide which type to purchase.

See attached file for full problem description.

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