For each of the following situations described below, select the distribution which best models the given situation (you may need to use some distributions multiple times). Provide a very short justification for your answer. Hypergeometric Uniform Chi-square Equally Likely Gamma Lognormal Poisson Binomial Exponential Chi-square Cauchy Weibull Geometric Negative Binomial Normal Lognormal Gamma F t Exponential Beta (a.) In an epidemiological study of the incidence of skin cancer for those individuals who use artificial tanning procedures, a researcher randomly selected 100 of the 10,000 customers of a large tanning facility. The 100 customers were examined and the number N who had developed skin cancer was recorded. The distribution of N is __? (b.) A civil engineer has determined that micro-cracks in bridge support columns occur according to a Poisson process with an average rate of 30 micro-cracks in a 10 feet length of column. She wants to assess the possible distance, D, between micro-cracks in a column. The distribution of D is _? (c.) In an epidemiological study of the incidence of chronic fatigue within those individuals who are fully employed and pursing a college degree, a researcher decided to interview 500 of the 100,000 students enrolled in a distance learning program at a well known university. The number S of students who had been diagnosed with chronic fatigue was recorded and used in the analysis. The distribution of S is (d.) A metallurgist designed a study to estimate the distribution of cracks in the cooling pipes at nuclear power plants. She randomly selected 200 sections of pipes within the cooling systems at various nuclear power plants. An x-ray is taken of each pipe and the number of cracks, C, of length greater than 20mm is recorded. A possible probability model for C, the number of cracks of length greater than 20mm in a randomly selected pipe, is . _?