Question: On March 12^th, 2007, the national average for a gallon of regular gasoline was $2.559 with a standard deviation of $0.3427. Suppose that we take a random sample of 45 gas stations and use the sample mean as a point estimate for the population mean national gas price

a) What is the distribution of all possible sample means?

b) What assumptions were made about the population when answering part (a)?

c) Determine the probability that the sampling error was less than $0.05

d) What effect would it have on the answer to part (C) if we increased our sample size? Explain

e) Suppose that our point estimate was from a sample of size 500 rather than of 45. Determine the probability that the sampling error would be less than $0.05