The annual precipitation in Tuscon, Arizona has been recorded over a 30-year period. The precipitation values are provided in the table below: Assume that each year's precipitation total is x¡

and the total number of years in the sample isn. You may use Excel to summarize the data. However, calculations must be shown on paper for credit. Summation calculations do not need to show all terms, but should indicate which terms in the table have been summed. \text { a) Calculate the precipitation sum as } \sum x_{i} \text { - } b) Determine the mean yearly precipitation. \text { Calculate the sum } \sum x_{i}^{2} \text { for the sample. } Determine the standard deviation of the sample. Group the data into approximately equal classes and construct a frequency distribution table. The precipitation ranges should include 0-3.9, 4-7.9, 8-11.9, 12-15.9, and >16 Draw a histogram of the distribution. You may present this chart using Excel output.