The graph of the annual snowfall distribution (in feet) for a particular county

Question

The graph of the annual snowfall distribution (in feet) for a particular county is shown below on the left with its mean and standard deviation. Assume that a sample size of 225 is drawn from the population. Determine which of the graphs labeled (a)-(c) would most closely resemble the sampling distribution of the sample means. Explain your reasoning. Choose the correct graph below. This graph most closely resembles the sampling distribution of the sample means, because mu_x- =, sigma_x- =, and the graph

Explanation / Answer

By central limit theorem, th mean is the same,

u(x) = 3.8 [ANSWER]

and a reduced standard deviation,

sigma(x) = sigma/sqrt(n) = 2.7/sqrt(225) = 0.18 [ANSWER]

So the correct graph is OPTION A. [ANSWER]

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