Question: Let X have a Poisson distribution with mean 16. Estimate P (X≥28) using the normal approximation.
I know that the normal distribution uses the mean and variance. In this case the standard deviation would be √16 which is ~ 4.
Do I just use Z=(x-μ)/σ to find the normal distribution? Which would come to be (28-16)/4 = 3. But that gives me Z and I'm not sure where to go from there.
For this same problem I also had to estimate using Chebyshev's inequality and came up with 1/9 so I'm assuming the normal distribution would give an estimate close to that. I'm just not sure how.