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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
and that the probability of a value falling between $a$ and $b$
P(a< x< b) = \int^b_a f(y)dy
Don't forget that the integral is the area under the curve between
Don't forget that you can look up the cumulative probabilities for
a normal distribution using tables.