In school, I was taught about the normal approximation to the binomial, and it was suggested that I could use it effectively under some conditions, because it can be 'easier to calculate'.
I understand how this could be more convenient if I were using paper tables. Are there still advantages to using the normal approximation when all my computations are done using computers? Is it easier to do algebraic manipulations or calculus using the approximation? What are some examples of the advantages?
I don't know what the right benchmark test would be, but perhaps this gives an idea:
> benchmark(rbinom(1, 1, .5), replications=1000000) test replications elapsed relative user.self sys.self user.child 1 rbinom(1, 1, 0.5) 1000000 3.593 1 3.476 0.156 0 sys.child 1 0 > benchmark(rnorm(1), replications=1000000) test replications elapsed relative user.self sys.self user.child 1 rnorm(1) 1000000 3.724 1 3.564 0.2 0 sys.child 1 0