This problem test is a series of questions related to the radon example we used in class. For Prof. Vogelsang's house in Haslett, n = 51 hourly radon measurements were taken in the winter of 2006. The sample average of those measurements is y = 1.68 and the sample variance is s = 0.851. For his former house in Ithaca, NY, n = 44 hourly radon measurements were taken in the winter of 1999. The sample average of those measurements is y = 4.19 and the sample variance is s2 = 0.3098. 1. Assuming that radon levels in the Ithaca basement follow a normal random variable with population mean Bo = 4 and population variance o2 = 0.42, compute the probabilities of the following events for Prof. Vogelsang's house in Ithaca: (a) The radon level goes below 2. (b) The radon level goes above 6. (c) The radon level is within 0.4 of the EPA cutoff of 4. (d) The radon level does NOT exceed the cutoff of 4. (e) The radon level is NOT within 0.4 of the EPA cutoff of 4.