1. ## Distribution Problem

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

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?

Futant.

2. Originally Posted by Futant
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