16. Argue, based on the central limit theorem, that a Poisson random variable having mean will...

16. Argue, based on the central limit theorem, that a Poisson random variable having mean λ will approximately have a normal distribution with mean and variance both equal to λ when λ is large. If X is Poisson with mean 100, compute the exact probability that X is less than or equal to 116 and compare it with its normal approximation both when a continuity correction is utilized and when it is not.

The convergence of the Poisson to the normal is indicated in Figure 6.5.