Hello, I am having trouble with this question as I am using the R code program, and I am unsure what I may be doing wrong.

The question:

2. Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 9 and a standard deviation of 1.5; Y has an expected value of 4 and a standard deviation of 0.3; Z has an expected value of 8 and a standard deviation of 1.1. Let T = 3X - 4Y -2Z Variable X Y Z Mean (Expected Value) 9 4 -8 Standard Deviation 1.5 0.3 1.1 Coefficient 3 -4 -2 a. What is the expected value of T? b. What is the variance of Y? c. What is the variance of T? d. What is the standard deviation of T? e. What is the probability that T is within 1.5 standard deviations of its mean? f. What is the probability that T is > 30? g. What is the probability that T is #2 Random Variable sum >ex Sigmax ey sigmay ez Sigmaz # T = 3*X-4*Y-2*Z (et (vy # t is normal with mean et & stdev sdt so want P(et-1.5*sdt pnorm(et + 1.5*sdt, et, sdt) - pnorm(et - 1.5*sdt, et, sdt) #e [1] 0. 8663856 1 - pnorm(30, et, sdt) #f Probability t >30 [1] 0.2801345 > pnorm(26, et, sdt) #g Probability t pnorm(30, et, sdt) - pnorm(26, et, sdt) #h Probability 26 qnorm(. 80, et, sdt) #i. 80th percentile of T [1] 31.33496 > .3513 #j L,M,S all # X + Z ~ N(ex + ez, sqrt(sigmax^2+sigmaz^2)) > (exy 07 \\:| b) What Is the expected value of T? c) What is the variance of T? d) What is the Standard deviation of T? e) What Is the probability that T ls wlthln 1.7 standard deviations of its mean. i) What is the probability than is > 9? 9) what is the probability that T is 5.7