I'm practicing statistics and I'm wondered how one can solve the following problem from Sage:
Find a numerical value of x such that 1√2π∫x−∞e−t2/2dt=0.987654321. I was thinking to different solutions:
1) Is there an inverse of normal distribution cumulative function?
2) Can we write it as f′(x)=e−x2/2,f(0)=1/2,f(x0)=0.987654321 and use some numerical method to solve the differential equation?
but I don't know are those functions implemented in Sage.