A total of 366 capsules, one for each day of the year, were placed in a vat. First, the January capsules were placed in the vat, then the ones for February, etc., with the ones for December going in last. The vat was then mixed (by turning it around for several minutes), and the capsules were then drawn out, one by one. The rst date drawn (September 14'th) was assigned rank 1, the second date drawn (April 24'th) was assigned rank 2, and so on. Those eligible for the draft who were born on September l4'th were called rst, followed by those born on April 24'th, and so on. On January 4'th, 1970, The New York Times ran an article, \"Statisticians Charge Draft Lottery Was Not Random\". To examine this claim, look at the le DraftLottery.MTP. The rst column contains the day of the year (1-3 66), the second column contains the rank for that day obtained in the lottery, and the third column contains the month for the given date. So, for example, the rst day of the year (Jan 1) received rank 305, and occurred in the rst month. A) Make a scatterplot of Rank (the Y variable) versus Dayonr (the X variable). Does this plot show any obvious patterns? B) Construct boxplots of Rank versus Month. Describe any patterns you see. Which month seems to be systematically receiving the lowest rankings (and therefore the largest chance of being draed)? Try to explain this phenomenon in terms of the description given above of the way the lottery was carried out