Normal Intersection

Age 16 to 18
Challenge Level

The probability density functions for two normal distributions are plotted on the same axes.

How many times can the two curves intersect? You might wish to start off using diagrams to aid your intuition, but be sure to justify your answers using reasoning from probability and algebra.

Did you know ... ?

Whilst diagrams are very useful tools at all levels of mathematics, 'diagrammatic fallacies', where incorrect properties of a mathematical object are intuited from a picture, are also common. When using a diagram in mathematics care always needs to be taken that these fallicies are avoided.