An interesting experiment was described in the paper "Sociochemosensory and Emotional Functions."† The authors of this paper wondered if college students could recognize their roommate by scent. They carried out an experiment in which female college students used fragrance-free soap, deodorant, shampoo, and laundry detergent for a period of time. Their bedding was also laundered using a fragrance-free detergent. Each person was then given a new t-shirt that she slept in for one night. The shirt was then collected and sealed in an airtight bag. Later, the roommate was presented with three identical t-shirts (one worn by her roommate and two worn by other women) and asked to pick the one that smelled most like her roommate. (Yes, hard to believe, but people really do research like this!) This process was repeated a second time, with the shirts refolded and rearranged before the second trial. The researchers recorded how many times (0, 1, or 2) that the shirt worn by the roommate was correctly identified. Suppose that instead of three shirts, each participant was asked to choose among five shirts and that the process was repeated five times. Then, assuming that the participant is choosing at random, x = number of correct identifications is a binomial random variable with n = 5 and p = 1 5 . (a) What are the possible values of x? (Enter your answers as a comma-separated list.) x = (b) For each possible value of x, find the associated probability p(x) and display the possible x values and p(x) values in a table. (Order your answers from smallest to largest x. Round your answers for p(x) to three decimal places.) x p(x) (c) Construct a probability histogram for the probability distribution of x. A histogram has a horizontal axis labeled "x" with values from 0 to 5 and a vertical axis labeled "p(x)" with values from 0 to 0.45. The histogram has 6 bars. Each bar is associated with a label and an approximate value as listed below. 1: 0 2: 0.01 3: 0.05 4: 0.21 5: 0.41 6: 0.33 A histogram has a horizontal axis labeled "x" with values from 0 to 5 and a vertical axis labeled "p(x)" with values from 0 to 0.45. The histogram has 6 bars. Each bar is associated with a label and an approximate value as listed below. 1: 0.33 2: 0.41 3: 0.21 4: 0.05 5: 0.01 6: 0 A histogram has a horizontal axis labeled "x" with values from 0 to 5 and a vertical axis labeled "p(x)" with values from 0 to 0.45. The histogram has 6 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0.33 1: 0.41 2: 0.21 3: 0.05 4: 0.01 5: 0 A histogram has a horizontal axis labeled "x" with values from 0 to 5 and a vertical axis labeled "p(x)" with values from 0 to 0.45. The histogram has 6 bars. Each bar is associated with a label and an approximate value as listed below. 0: 0 1: 0.01 2: 0.05 3: 0.21 4: 0.41 5: 0.33 You may need to use the appropriate table in the appendix or technology to answer this question.