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## 'Into the Normal Distribution' printed from http://nrich.maths.org/

You might like to recall that the pdf of an $N(\mu, \sigma^2)$
random variable is

$$

f(x) =\frac{1}{\sqrt{2\sigma
^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}

$$

and that the probability of a value falling between $a$ and $b$
is

$$

P(a< x< b) = \int^b_a f(y)dy

$$

Don't forget that the integral is the area under the curve between
two points.

Don't forget that you can look up the cumulative probabilities for
a normal distribution using tables.