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Probability of normal variable and its standardized version different?

Dear community members, May I know why Mathematica returns different values when computing the probability of a random normal variable and its standardized equivalent? For example:

In[59]:= NProbability[y < 46, 
 y \[Distributed] NormalDistribution[43, 9]]

Out[59]= 0.630559

compared to:

In[2]:= NProbability[y < 1, y \[Distributed] NormalDistribution[]]

Out[2]= 0.841345
POSTED BY: Ruben Garcia Berasategui
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You are asking for the probability of y < mu+sigma for your random normal variable this is the value 52.

In[14]:= NProbability[y < 1, y \[Distributed] NormalDistribution[]] ==
  NProbability[y < 52, y \[Distributed] NormalDistribution[43, 9]]

Out[14]= True

or you should compare it to the probability of y<1/3

In[16]:= NProbability[y < 1/3, 
  y \[Distributed] NormalDistribution[]] == 
 NProbability[y < 46, y \[Distributed] NormalDistribution[43, 9]]

Out[16]= True
POSTED BY: Martijn Froeling

Hi Martijn, thanks for the explanation. I assumed that the second argument was the variance. Regards, Ruben
POSTED BY: Ruben Garcia Berasategui
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