The 80-year record of annual precipitation at Lincoln, Nebraska, yields a range of values between 10 and 50 in. with a mean annual value of 25.00 in. and a standard deviation of 5.30 in. Because annual precipitation represents a sum of many random variables (i.e., depth of precipitation for each day of the year), assume that annual precipitation is normally distributed.
(a) In 1936 the precipitation at Lincoln was a mere 14 in. Determine the probability that the annual precipitation will be 14 in. or less next year.
(b) In 1965 Lincoln received 42 in. On the average, this amount would be equaled or exceeded once in how many years?
(c) Compare the theoretical and apparent return periods of the record-high value of 50.00 in.
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