The three additional points are just too close together with respect to the curve. As for your second attempt, here is how to show the three points:
Show[Plot[PDF[NormalDistribution[0, 1], x], {x, -5, 5}],
NumberLinePlot[{0.0425371, 13/147, 0.134334}],
PlotRange -> All]
The function NumberLinePlot places its points at y=1.
