1. In a large group of corporate executives, 10% have no college education, 20% have exactly 2 years of college, 30% have exactly 4 years, and 40% have 6 years. A sample size of 2 (with replacement) is to be taken from this population. Find the sampling distribution of the mean number of years in college of the executives in the sample.
2. The daily catch of a small tuna-fishing fleet averages 130 tonnes. The fleet's logbook shows that the weight of the catch varies from day to day and this variation is measured by the standard deviation of the daily catch, s = 42 tonnes. What is the probability that during a sample of n = 36 fishing days, the total weight of the catch will be 4,320 tonnes or more?