A chemical test involves measuring two independent quantities, A and?

Question

A chemical test involves measuring two independent quantities, A and
B, and then expressing the result of the test as C, where C = A− 1
4B.
If A is normally distributed with mean 9 and standard deviation 1, and
B is also normally distributed with mean 32 and standard deviation 3,
what proportion of C values would you expect to be negative?

sorry , the correct c=A-1/4*b

Answer 1

C will also be normal

meanC = E(A) - 1/4E(B)
=9 - 8 = 1

VarC = 1 + (1/16)(9) = 25/16 => std. dev. = 5/4

P(C < 0) = (0 - 1)/(5/4) = -4/5 = -0.80

Then use your standard normal to find P(Z < -0.8) = P(Z > 0.8)