Reference no: EM1317053

Q1) Bill and George go target shooting together. Both shoot at target at same time. Assume Bill hits target with prob. 0.7, George, independently, hits the target with prob. 0.4.

a) Now both of them shoot once and exactly one shot hits the target. Determine the probability that it was George's shot?

b) Now both of them shoot once and target is hit. Determine the probability that George hit it?

Q2) Suppose that federal regulations need that average smoke stack concentration of certain industrial pollutant should not exceed 135 ppm.  Environmental Protection Agency suspects that one factory is violating this requirement.  Environmental Protection Agency randomly gathers 31 independent specimens of smoke from factory's stack, one specimen on each day in October, and performs an accurate (and expensive!) lab analysis.  Results in ppm are: 147,151,122, 107,136,139, 141,153, 138,111,155, 147,165,148,150, 123, 106,137, 138,142,154,139, 109, 157, 146, 168,145, 153, 120,104, and 130.

Q3) Explain how each party (the factory management and Environmental Protection Agency) might argue its case based on sound statistical reasoning. Suppose that each party has statistically competent advisers. i.e., each party's position must be statistically sound.  Include as suitable graphs, computations, and statistical tests.