Find the z score boundaries that separate a normal distribution as described

If you know the mean you know the standard deviation. Take your data point, subtract the mean from the data point and then divide by your standard deviation. That gives you your Z-score.

The correspondence between these boundaries is z=x−μσ, where z is the boundary for the standard normal pdf, and x is the boundary for the unknown normal pdf. To find the boundaries corresponding to 4 and 3, you can use GeoGebra.

Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve). In order to use a z-score, you need to know the mean μ and also the population standard deviation σ.

For the given normal distribution, the top 2.5% would be scores above 12.87 (1.96 standard deviations above the mean).