Then, it should make sense that the probability that a given measurement reveals a result between x and x+dx is f(x)dx. So the total probability to get a result between <i>any<\i> two points is just the integral from the lower point to the upper point of f(x) (the area under your normal distribution between those two points). The trouble is that I don't think you can symbolically integrate your normal distribution. A couple ways you can proceed is to
a) make an approximation (say, Taylor expansion) and work with that
b) Use a computer and find your answer numerically
c) Just look up what the values are in a table and believe them because someone else has already done this work for you!
How can I prove this?
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