We have
[tex] \mu = 500[/tex]
[tex] \sigma = 100 [/tex]
425 corresponds to a z of
[tex]z_1 = \dfrac{425 - 500}{100} = -\dfrac 3 4[/tex]
575 corresponds to
[tex]z_2 = \dfrac{575 - 500}{100} = \dfrac 3 4[/tex]
So we want the area of the standard Gaussian between -3/4 and 3/4.
We look up z in the standard normal table, the one that starts with 0 at z=0 and increases. That's the integral from 0 to z of the standard Gaussian.
For z=0.75 we get p=0.2734. So the probability, which is the integral from -3/4 to 3/4, is double that, 0.5468.
Answer: 55%
