How do I calculate the capacitance in this circuit?
you know
  C=Ic * dt/dV  with dV = 4 , dt = 10ms,  Ic=Vavg/R , Vavg = Vmax-min   

let  Vf diode = 0.7  x2   

Often rated AC RMS out voltage includes 10% XFMR loss but that would be bonus points maybe... Which affects N but assume ideal here and remember this is peak  AC given for input and not  RMS which is only 70.7% of that.