Statistical Properties of the Normal Distribution Explained?

Question

The following is a question regarding statements from "Chemical Fate and Transport in the Environment" 2e by Hemond and Fechner-Levy pg. 78. I do not understand point #2 that follows, if anyone can point me to a proof or literature that explains this property I'd greatly appreciate it!

1) "It follows from the properties of the normal distribution that the portion of the distribution within one standard deviation of the mean value (both + and -) includes 68% of the possible values. [I understand this]

2) "It also follows that the value at one standard deviation from the mean value is equal to the mean value multiplied by 0.61" [This is the statement I am having trouble understanding]

Thanks!

Anonym · Answer

In general statement 2 must be false.  For example, there are normal distributions with mean = 0.  Statement 2 would imply that one standard deviation from the mean would also = 0

Davis P · Answer

at one sigma e^(-1/2) = 0.60653066
which rounds to 0.61

Statistical Properties of the Normal Distribution Explained?

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