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About the normal probability distribution: with formula

P(X=x) = (1/(σ*sqrt(2π))*exp(-(x-μ)^{2}/2σ^{2}), what happens when you look at P(X=μ) if σ<(1/sqrt(2π))? You get P(X=μ)>1, an absurdity. What is going on?

Second question is one about intuition: suppose μ=0, then why would a scale change of the horizontal axis (say by changing units from meters to kilometers) , which would also change σ, affect the probability of the mean, which it would by the formula?

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# P(x=mean) of normal PDF with low sigma - not allowed?

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