I have a question on a take-home that asks:
Find a value such that (X is normally distributed rv) :
P (μ -σ < X< μ + βσ) = 0.95
I must be doing something wrong, though, because from everything I can tell, this is impossible.
When standardized, this would lead to:
z1= x-μ /σ = μ -σ - μ / σ = -1
leading me to:
P(z< z2) = 0.95 + P(z < -1)
0.95 + P(z < -1) has a value of greater than 1, which is obviously impossible. Am I doing this wrong, or does this question have no answer?
Thank you for your help, in advance!