Examine the probability distribution shown below. Complete parts a through d. x 5 10 15 20 25 30 35 4D 45 50 @ P(x) 0.02 0.06 0.15 0.15 0.25 0.10 0.16 0.03 0.03 0.05 a. Calculate the expected value and standard deviation for this random variable. E(x) = Cl (Type an integer or a decimal.) 0x = Cl (Round to two decimal places as needed.) b. Denote the expected value as (1. Calculate p - 6 and p + a. p - a = D (Round to two decimal places as needed.) p + 0' = D (Round to two decimal places as needed.) c. Determine the proportion of the distribution that is contained within the interval p :t: 6. E (Type an integer or a decimal.) d. Repeat part c for (1) p. :t: 25 and (2) p. :t 30. (1) Determine the proportion of the distribution that is contained within the interval pi 25. E (Type an integer or a decimal.) (2) Determine the proportion of the distribution that is contained within the interval pi 36. E (Type an integer or a decimal.)