Examine the probability distribution shown below. Complete parts a through d. X 5 10 15 20 25 30 35 40 45 50 P(x) 0.02 0.06 0.13 0.20 0.30 0.15 0.03 0.04 0.01 0.06 a. Calculate the expected value and standard deviation for this random variable. E(x) = (Type an integer or a decimal:) 5x =(Round to two decimal places as needed.) b. Denote the expected value as u. Calculate u - o and p + o. H -o= (Round to two decimal places as needed.) u += (Round to two decimal places as needed.) c. Determine the proportion of the distribution that is contained within the interval pito. (Type an integer or a decimal.) d. Repeat part c for (1) u + 20 and (2) u + 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 p 1 36. (Type an integer or a decimal.)