1) (3 points) Suppose you wish to study the prevalence of tobacco use among undergraduate students at UofL. A total of 1,445 randomly sampled undergraduate students at UofL were selected to participate in your study. The table below summarizes some of the data collected from the subjects in your study. The rows represent "tobacco use" and the columns represent "class status". Class status Freshman Sophomore Junior Senior Total Tobacco user 36 35 37 52 160 Non-user 322 268 296 399 1285 Total 358 303 333 451 1445 Use the table above determine the following probabilities in both fraction and decimal form. Show your work. a) (0.5 points) P(Tobacco user | Sophomore) = ? b) (0.5 points) P(Non-user | Sophomore) = ? c) (0.5 points) P(Sophomore) = ? d) (0.5 points) P(Sophomore | Tobacco user) = ? e) (0.5 points) P(Senior | Non-user) = ? f) (0.5 points) P(Senior and Tobacco User) = ? 2) (4.5 points) A new screening test for colon cancer is going through testing to see if it is accurate enough to be widely used. A clinical trial has been run with 300 patients aged 40-49 with high risk of colon cancer. The data is summarized in the following table. Colon Cancer No Colon Cancer Total Screen + 63 24 87 Screen - 32 191 223 Total 95 215 N = 300 Use the table above determine the following quantities in both fraction and decimal form. a) (0.5 points) Prevalence of colon cancer in this population b) (0.5 points) Sensitivity of the test c) (0.5 points) Specificity of the test d) (0.5 points) Positive predictive value of the test e) (0.5 points) Negative predictive value of the test f) (0.5 points) False positive fraction of the test g) (0.5 points) False negative fraction of the test h) (1 point) Do you think that this is a good test? Justify your answer by considering some of the above quantities.3) (3 points) Of the possible terms in question 2 (prevalence, sensitivity, specificity, positive predictive value, negative predictive value, false positive fraction, false negative fraction), which term represents the relevant probability for each scenario? Do not compute the probabilities, just name the term in words. a) (0.5 points) Alice received a negative test result. Which quantity represents the probability that Alice does not have colon cancer? b) (0.5 points) Bob has colon cancer. Which quantity represents the probability that his test will come back positive? c) (0.5 points) Charlotte has yet to receive her test result. What quantity represents the probability that Charlotte has colon cancer? d) (0.5 points) Daniel has colon cancer. Which quantity represents the probability that his test will come back negative? e) (0.5 points) Eliza received a positive test result. Which quantity represents the probability that Eliza has colon cancer? f) (0.5 points) Flynn does not have colon cancer. Which quantity represents the probability that his test will come back negative? 4) (3.5 points) The probability of hypertension (high blood pressure) for Americans aged 18-39 is approximately 0.22. Suppose that 8 Americans aged 18-39 are randomly sampled, and each is tested to determine whether or not they have hypertension. a) (1.5 points) List the 3 assumptions for a binomial distribution and determine whether they are satisfied in this scenario. b) (0.5 points) We will assume that X ~ Bin(n,p) for this context. What are the values of n and p? c) (0.5 points) What is the mean of this binomial distribution? d) (0.5 points) What is the variance of this binomial distribution? e) (0.5 points) What is the standard deviation of this binomial distribution? 5) (5 points) The probability of hypertension (high blood pressure) for Americans aged 18-39 is approximately 0.22. Suppose that 8 Americans aged 18-39 are randomly sampled and tested for hypertension. x = # who test positive 3 5 7 8 for hypertension Probability a) (2.5 points) Use Excel to fill in the probabilities in the table above. Round to 4 decimals.Homework 3: 20 points Due: 9/30/22 11:59 PM b) (0.5 points) What is the probability that none of the respondents have hypertension? c) (0.5 points) What is the probability that at least two respondents have hypertension? d) (0.5 points) What is the probability that between 3 and 5 respondents (3