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**1. Homework Statement**

Let Z be a standard normal random variable and [tex]\alpha[/tex] be a given constant. Find the real number x that maximizes P(x < Z < x + [tex]\alpha[/tex])/

**2. Homework Equations**

**3. The Attempt at a Solution**

Looking at the standard normal tables, it seems obvious to me that x=0 gives the largest spread regardless of the value of the constant, but I am not sure how to find this computationally. Can anyone give me a hint on what direction to take? Thanks for any help.

I got most of the rest of the homework done, but the three I just posted really have me stumped.