The result for the given normal random variables are as follows;
a. E(3X + 2Y) = 18
b. V(3X + 2Y) = 77 
c. P(3X + 2Y < 18) = 0.5
d. P(3X + 2Y < 28) = 0.8729
<h3>What is normal random variables?</h3>
Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.
Now, according to the question;
The given normal random variables are;
E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.
Part a.
Consider E(3X + 2Y) 

Part b. 
Consider V(3X + 2Y) 

Part c. 
Consider P(3X + 2Y < 18) 
A normal random variable is also linear combination of two independent normal random variables.

Thus,

Part d. 
Consider P(3X + 2Y < 28)


Therefore, the values for the given normal random variables are found.
To know more about the normal random variables, here
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The correct question is-
X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following: 
a. E(3X + 2Y) 
b. V(3X + 2Y) 
c. P(3X + 2Y < 18) 
d. P(3X + 2Y < 28)