Final answer:
The sampling distribution of (p) hat can be approximated by a normal distribution when certain conditions are met. In this case, the distribution of (p) hat, with n = 20,000 and p = 0.3, can be approximated by a normal distribution with mean equal to the population proportion and standard deviation equal to the square root of (p)(1-p)/n.
Step-by-step explanation:
The sampling distribution of (p) hat can be approximated by a normal distribution when certain conditions are met. The conditions for using a normal distribution approximation for a sample proportion are: a random sample, independence between observations, and both np and n(1-p) being greater than 5. In this case, the sample proportion (p) hat has n = 20,000 and p = 0.3. Since the sample size is large (n=20,000), the sampling distribution of (p) hat can be approximated by a normal distribution with mean (mu) equal to the population proportion (p), and standard deviation (sigma) equal to the square root of (p)(1-p)/n.