2. At Bobcat Jensen’s grocery store, there has been a pandemic-induced rush on certain goods, such as • T: packages of toilet paper • W: packages of disinfectant wipes The following joint distribution shows how many packages of toilet paper and disinfectant wipes a shopper can obtain per visit. Compute the requested probabilities for one shopping visit. T 0 1 2 3 W 0 0.31 0.22 0.09 0.04 1 0.15 0.05 0.04 0.01 2 0.04 0.03 0.01 0.00 (a) probability that zero packages of toilet paper and zero packages of disinfectant wipes are purchased (b) expected number of packages of toilet paper purchased (c) standard deviation of packages of disinfectant wipes purchased given that exactly one case of toilet paper was obtained

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