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Suppose that over a certain period prices of stocks in the S&P 500 can be approximately modeled using the normal distribution with $\mu = \$40.35$ and a standard deviation of $\$8.97$. The data file (attached) has a random sample of $50$ prices. Use the DAT Descriptive Statistics to analyze the sample. Note that in general the sample should reflect the properties of the population. Does this model seem plausible based on the sample statistics? The most relevant are mean, standard deviation or variance, skewness and kurtosis.

DAT Figures:

\begin{array}{l|r} \bf\text{Stock} & \bf\text{Prices} \\ \hline \text{Mean} & 41.17814 \\ \text{Standard Error} & 1.356304 \\ \text{Median} & 41.99538 \\ \text{Mode} & \text{#N/A} \\ \text{Standard Deviation} & 9.590518 \\ \text{Sample Variance} & 91.97803 \\ \text{Kurtosis} & -0.17833 \\ \text{Skewness} & -0.35956 \\ \text{Range} & 41.58691 \\ \text{Minimum} & 17.20985 \\ \text{Maximum} & 58.79676 \\ \text{Sum} & 2058.907 \\ \text{Count} & 50 \end{array}

So my question is what exactly is my professor looking for?

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closed as unclear what you're asking by Did, Davide Giraudo, Brevan Ellefsen, Daniel W. Farlow, user91500 Apr 16 '17 at 5:27

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You are told what the mean and standard deviation of a large distribution of prices is. You have now drawn fifty samples. You should have a formula for how closely the mean of your samples should be to the mean of the whole distribution. Is this within that? How likely is it that your measured mean would be at least this far from the true mean. Similarly, you should have a formula for how closely your sample standard deviation matches the real standard deviation. Are they as close as you would expect? Do these calculations and comment on the results.

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