Question

scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100% of people who write this exam obtain scores between 425 and 575​

Answer 1

We have

$\mu = 500$

$\sigma = 100$

425 corresponds to a z of

$z_1 = \dfrac{425 - 500}{100} = -\dfrac 3 4$

575 corresponds to

$z_2 = \dfrac{575 - 500}{100} = \dfrac 3 4$

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%