For a normal random variable X with a mean of 12 and a standard deviation of 3, find a number x0 such that the following probabilities are obtained:
a) P(X <= x0) = 0.5
b) P(X >= x0) = 0.23
My solutions:
a) To normalize X, I did (x0-12)/3 = 0 because the Z-value for 0.5 is 0. Solving for x0, I got x0 = 12.
b) Since X>= x0, I wasn't sure if you could solve the problem the same way as in part a. How would I solve part b?
a) P(X <= x0) = 0.5
b) P(X >= x0) = 0.23
My solutions:
a) To normalize X, I did (x0-12)/3 = 0 because the Z-value for 0.5 is 0. Solving for x0, I got x0 = 12.
b) Since X>= x0, I wasn't sure if you could solve the problem the same way as in part a. How would I solve part b?