I am having trouble with this question. I am using the R programing language and having trouble in both creating the code and solving the question:

Round decimal answers to at least 3 places unless otherwise instructed. Answer all numeric questions to at least 3 decimal places unless the number has fewer digits or you are otherwise instructed. Do not round too early. E.g. 18 is input as 18. .32 is entered as .32 etc. The rounding rules are that you must be accurate to within .001 of the correct answer

Suppose the amount, a, of impurity A in a vat of hot caramel is normally distributed with mean 21 and standard deviation 4, the amount, b, of impurity B in the vat of hot caramel is normally distributed with mean 12 and standard deviation 3, and the amount, c, of impurity C in the vat of hot caramel is normally distributed with mean 16 and standard deviation 8. a, b, and c are independent of one another. Let X = total impurity be defined by X = a + b + c. Let W = weighted impurity be defined by W = 3a + 4b - 2c a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) Calculate the variance of W. e) If we pick a value k such that the probability that X > k equals .20 then calculate k? f) The hot caramel is considered impure if X > 53. What is the probability the hot caramel is impure? g) What is the probability that X is within one standard deviation of its expected value? h) What is the probability that a is greater than b? i) What is the probability that a, b, and c are all greater than their expected values