Problem 1 a pond contains 42 fish. seven are caught, tagged, and released back into the pond. after the tagged fish have had a chance to mingle with the others, seven fish are caught and released, one at a time. assume that every fish in the pond is equally likely to be caught each time, regardless of which fish have been caught (and released) previously (this is not a realistic assumption for real fish in a real pond). the chance that among the fish caught in the second stage (after the tagging), at least zero and at most three were previously tagged is (q1)

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to