Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. x P(x) 0 0.363 1 0.433 2 3 0.179 0.025 No, the random variable x is categorical instead of numerical. D. No, the sum of all the probabilities is not equal to 1. E. No, the random variable x's number values are not associated with probabilities. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = 0.9 adult(s) (Round to one decimal place as needed.) B. The table does not show a probability distribution. Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. = adult(s) (Round to one decimal place as needed.) B. The table does not show a probability distribution. 3 When playing roulette at a casino, a gambler is trying to decide whether to bet $5 on the number 19 or to bet $5 that the outcome is any one of the three possibilities 00, 0, or 1. The gambler knows that the expected value of the $5 bet for a single number is -53. For the $5 bet that the outcome is 00, 0, or 1, there is a probability of of making a net 35 profit of $15 and a 38 probability of losing $5. 38 a. Find the expected value for the $5 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $5 bet on the number 19 or a $5 bet that the outcome is any one of the numbers 00, 0, or 1? Why?