3. a manager asked her employees how many times they had given blood in the last year. the results of the survey are given below. the random variable x represents the number of times a person gave blood. show all setups and work by hand. x. plx) p(x) 0.30 1 0.25 0.25 a.25 2 0.20 3 0.12 1,08 1.12 6.20 6.28 o.2 4 0.07 5 0.04 0.02 tl. o 4.97 l: 1 a) does the given information describe a probability distribution? explain why by checking requirements. (2 points) b) find the probability of randomly selecting an employee having donated blood at least three times. (2 points) c) using the formula, find the expected value of the number of times an employee donated blood. show all your work and steps. if necessary, expand the table above. round to one decimal place. (3 points) d) using the formula, find the standard deviation of the distribution. show all your work and steps. if necessary expand the table above. round to one decimal place. (3 points) e) use the range rule of thumb to determine if it is unusual for an employee to have donated blood five times? explain or show how you came about that conclusion. (2 points) pl) o. 12 1