pgfmathdeclarefunction{gauss}{3}{%
  pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}
}

begin{tikzpicture}
  % normal distribution PDF
  addplot [thick] {gauss(x,0,1)};
  % right vertical line
  pgfmathparse{gauss(+1.96,0,1)};
  pgfmathsetmacropgftempapgfmathresult;
  node[coordinate] (a) at (axis cs:+1.96,pgftempa) {};
  draw (axis cs:+1.96,0) -- (a);
  % left vertial line
  pgfmathparse{gauss(-1.96,0,1)};
  pgfmathsetmacropgftempbpgfmathresult;
  node[coordinate] (b) at (axis cs:-1.96,pgftempb) {};
  draw (axis cs:-1.96,0) -- (b);
end{tikzpicture}

newcommand{evaluatefunction}[1]{%
  pgfmathparse{#1)};
  pgfmathsetmacropgftempapgfmathresult;
}
node[coordinate] (a) at (axis cs:+1.96,evaluatefunction{gauss(1.96,0,1)}) {};