Exercise 2
josie will soon be taking exams in math and spanish. she estimates that the probability she passes the math exam is 0.9, and the probability that she passes the spanish exam is 0.8.
she is also willing to assume that the results of the two exams are independent of each other.
a. using josie’s assumption of independence, calculate the probability that she passes both exams.
b. find the probability that josie passes at least one of the exams. (hint: passing at least one of the exams is passing math or passing spanish.)

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