(a) No.
Sample means have a narrower distribution that is inversely proportional to the square root of the number of samples in the group.
(b) Assume the distribution mean of samples of 9 has a mean of 80.04 with a standard deviation of 1.58
I get 63.7% for the probability.
Statistical Abstracts (117th edition) reports sale price of unleaded gasoline (in cents per gallon) at the refinery. The distribution is mound-shaped with mean μ = 80.04 cents per gallon and standard deviation, σ = 4.74 cents per gallon.
(a) Are we likely to get good results if we use the normal distribution to approximate the distribution of sample means for samples of size 9? Explain.
(b) Find the probability that for a random sample of size 9, the sample mean price will be between 79 and 82 cents per gallon.
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