The onesample ztest for proportions determines the pvalue us

The one-sample z-test for proportions determines the p-value using the “normal approximation method”. This method approximates the exact p-value that would have been found if the binomial formula were used. But, the “normal approximation method” only works well when the sample size is “large enough”. Why is the one- sample z-test for proportions used instead of just using the binomial formula to find p-values? Do you think it is necessary to use the one-sample z-test for proportions for “large sample sizes” with the advent of technology? That is, should we always use the binomial formula to find p- values when we have a binomial random variable and one population even if the sample size is “large”? Explain.

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