Final answer:
The sampling distribution of p-hat represents the distribution of sample proportions. It approximates a normal distribution if the sample size is large enough.
Step-by-step explanation:
The sampling distribution of p-hat is the distribution of sample proportions. It represents all possible sample proportions that could be obtained from a population. The shape of the sampling distribution of p-hat is approximately normal if the sample size is sufficiently large. In this case, the size of the population is 15,000, which is not mentioned.
Example: If we take random samples of size 100 from a population and calculate the proportion of success, say the proportion of students who passed the exam, we would have a sampling distribution of p-hat. It would approximate a normal distribution with a mean equal to the population proportion p and a standard deviation equal to the square root of (p(1-p)/n), where n is the sample size.