4. As sample size increases, the distribution of a sample should approach the location, scale, and shape of its underlying probability distribution. If we assume that all four quarters of student data are sampled from the same population, do you think that the Gumbel distribution provides a reasonable approximation of the underlying probability distribution for this variable? 'Why or why not? 5. The last histograms on pages 4 through 8 do not describe the distribution of a single sample but instead the distribution of 50,DDD sample averages (i.e. the sample averages calculated for 50,00 separate samples). What is the name of the probability distribution toward which the distributions of sample statistics such as this converge as the number of identically generated samples approaches innity? 6. Do you think that the Gumbel distribution provides a reasonable approximation of the probability distribution toward which these distributions of sample averages converge as the number of samples approaches infinity? Why or why not? If not, what distribution might be a better candidate model be? My? 'F'. If the tted Gumbel distribution is a good model for the combined student data, the sample averages calculated for a real sample should fall within a typical range of sample averages resulting from that model. Based on the last histogram on pages 4 through 8, does the fitted Gumbel distribution appear to be a good model for each quarter's sample, as well as for the combined sample? 'Why or why not