Random Sample of size n500 were selected from a binomial pop

Random Sample of size n=500 were selected from a binomial population with p=0.1? a) is it appropriate to use the normal distribution to approximate the sampling distribution of p? check to make sure the necessary conditions are met.

Solution

To use the normal distribution to approximate the sampling distribution of p there must be 10 expected successes and 10 expected failures, n * p > 10 and n * (1-p) > 10.
In this case:
n * p = 500 * 0.1 = 50 expected success
n * (1 - p) = 500 * 0.9 = 450 expected failures

So, there are enough expected successes and expected failures. Hence it is appropriate to use the normal distribution to approximate the sampling distribution of p because the necessary conditions are met.