Integrating a normal distribution many times

[Søren Hauberg]

Hi,
  This is not necessarily an Octave question. but here goes anyway.
  I need to evaluate the integrate a normal distribution over a 
specific interval with many mean values. My current Octave 
implementation just calls 'quad' at mean value, i.e.

for t = linspace(0, 32, 750)
  qq = @(x) normal_pdf(x, t, 2.5);
  result = quad(qq, 19, 26, 0)
endfor

This is, however, fairly slow. At some point my system needs to run in 
real-time (not in an Octave implementation), so I doubt that the above 
strategy will work. Does anybody have some hints on how to speed this 
up? Should I precalculate a lookup table with some values and then 
interpolate when I need to evaluate the function at a new mean value?

Søren