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'Weekly Challenge 40: Normal Intersection' printed from http://nrich.maths.org/
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
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.