Two normal curves with different standard deviations must still have equal:

1. Every probability distribution carries total probability one. 2. If the total area under each curve is one, the two curves are directly comparable as probabilities. 3. Since the area under the curve must equal one, a change in the standard deviation causes a change in the shape of the curve. 4. The curve becomes fatter or skinnier depending on the deviation, so the peaks differ. 5. Only the enclosed area is forced to match. _Source: OpenStax Introductory Statistics 2e (CC BY 4.0), Ch 6 'The Normal Distribution', sections 6.1-6.3_