Percentiles

NOTE: "StdDev" simply specifies a starting value for the "FindRoot" search.  As with all numerical solvers, FindRoot is somewhat sensitive to the choice of this initial values; if the answer provided does not make sense, try another starting point as a check.
  Since the Normal is a symmetric distribution, using the expected value as the starting point can result in some confusion. Hence in this case we choose to start at one standard deviation.

In[24]:=

p = .95 ;

FindRoot[F[xstar, μ, σ] == p, {xstar, StdDev}]

Out[25]=

{xstar→41.9813}

In[308]:=

End[(* NormalProperties` *)]

Out[308]=

NormalDistribution`


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