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The standard normal curve is φ(z) = 1/(√(2π)) e^(-z²/2).
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The standard normal curve is . The area under it between and is the share of the data that lies within standard deviations of the mean. Use quad to find this share for and .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Write the function, and integrate it from to .
Check. This is the "68, 95, 99.7 rule" of statistics: about 68 percent of normal data is within one standard deviation of the mean, about 95 percent is within two, and about 99.7 percent is within three. The integral of the whole curve over is exactly 1, which you can check with np.inf as the limits.
Answer: 0.6827, 0.9545 and 0.9973.
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