*** I'll leave it to others to decide whether 0.9717 and 0.9786 are more than slightly different, ***
You SHOULD NOT leave to others but to THINK ABOUT. The way I posted is the *one* when the signal o the error I unimportant. You made an error of analysis: it is not throughout the Z values that the errors must be chosen but by the associated tail probabilities, evidently. *********************
*** But i find this curious: are you really saying that one must use the Normal approximation with a continuity correction, rather than the exact binomial calculation? If so, why? And why can't this be disputed? ***
OF COURSE NOT: I didn?t and I?ll never say such nonsense.
The reason by which the normal approximation is used is that is immediate. On contrary the exact way needs computer programming. If available, do not hesitate: use it. If not, the only *decent* way is to use the continuity correction.