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

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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.