A random variable X is Normally distributed with mean = 75 and = 8.Let Y be a second Normally distributed random variable with mean = 70 and = 12.It is also known that X and Y are independent of one another.Let W be a random variable that is the difference between X and Y (i.e. ,W = X - Y).What can be said about the distribution of W?
A)W is N(0,20)
B)W is N(5,20)
C)W is N(5,-4)
D)W is N(5,14.4)
E)W is N(0,14.4)

Question

A random variable X is Normally distributed with mean  = 75 and  = 8.Let Y be a second Normally distributed random variable with mean  = 70 and  = 12.It is also known that X and Y are independent of one another.Let W be a random variable that is the difference between X and Y (i.e. ,W = X - Y).What can be said about the distribution of W?
A)W is N(0,20) 
B)W is N(5,20) 
C)W is N(5,-4) 
D)W is N(5,14.4) 
E)W is N(0,14.4)

Quizplus · Accepted Answer

Since X and Y are independent, their difference W will also be Normally distributed, with mean E(W) = E(X) - E(Y) = 75 - 70 = 5. The variance of W is Var(W) = Var(X) + Var(Y) = 8^2 + 12^2 = 208. Therefore, the standard deviation of W is sqrt(208) = 14.4. So the distribution of W is N(5,14.4).

A Random Variable X Is Normally Distributed with Mean