Over roughly the past 100 years, the mean monthly April precipitation in Williams town, Massachusetts, equaled 3.6 inches with a standarddeviation of 1.6 inches. (Source: http://web.williams.edu/  weather/)
a. In April 1983, the wettest April on record, the precipitation equaled 8.4 inches. Find its z-score. If the distribution of precipitation were roughly normal, would this be unusually high? Explain.
b. Assuming a normal distribution, an April precipitation of 4.5 inches corresponds to what percentile?
c. Of the 119 measurements of April precipitation on record (reaching as far back as 1892), 66.5% fell within one, 97.5% within two, and 99.1% within three standard deviations of the mean. Do you think that the distribution of April precipitation is approximately normal? Why or why not?