12 20 30 P(x) 0.01 0.05 0.13 0.25 0.25 0.20 0.02 0.03 0.02 0.04 a. Calculate the expected value and standard deviation for this random variable. E(x) = (Type an integer or a decimal.) ox = (Round to two decimal places as needed.) b. Denote the expected value as u. Calculate u - o and u + 6. H - = (Round to two decimal places as needed.) H += (Round to two decimal places as needed.) c. Determine the proportion of the distribution that is contained within the interval u to. (Type an integer or a decimal.) d. Repeat part c for (1) u + 20 and (2) | + 30. (1) Determine the proportion of the distribution that is contained within the interval u + 20. (Type an integer or a decimal.) (2) Determine the proportion of the distribution that is contained within the interval u + 30. (Type an integer or a decimal.) Next