I had a question about an instantaneous z score. The question reads as P ( z = 2 )I think that this is 0, as z-score is the area under the curve and could be found by integrating the PDF over the range. As the range is 0, the area is also zero. Is that correct?

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I had a question about an instantaneous z score. The question reads as  P  (  z  =  2  )I think that this is 0, as z-score is the area under the curve and could be found by integrating the PDF over the range. As the range is 0, the area is also zero. Is that correct?

isscacabby17 · Accepted Answer

Since   P  (  z  =  2  ) is the same as      1          2      π            ∫    2    2    exp  ⁡      (    −                  u        2            2        )        d    uthen yes, the result is zero; this can be interpreted also as saying      1          2      π            ∫          −      ∞        2    exp  ⁡      (    −                  u        2            2        )        d    u  −      1          2      π            ∫          −      ∞        2    exp  ⁡      (    −                  u        2            2        )        d    uvia the Fundamental Theorem of Calculus.Geometrically, the &quot;integral&quot; covers no area on the Gaussian curve, which agrees with the result of 0.

I had a question about an instantaneous z score. The question reads as P ( z = 2

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