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What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
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There is a 68–95–99.7 rule for a normal random variable.

Beyond one standard deviation, we have 31.8% of the points.

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What u said...I don't understand
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For standard Random normal distribution variable, the graph looks like this

normal curve

Normal random variable differs from its mean μ by more than σ = (same as saying) = Area under the graph (-infinity to σ) + (σ to infinity)= 100-68.26 = 31.74 i.e. probability of 0.3174  

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