Final answer:
True, the sampling distributions for p^ become more bell-shaped as the sample size increases, especially when p is near 0.5. This relates to the central limit theorem and the normal distribution's characteristics according to the empirical rule.
Step-by-step explanation:
True, for samples of size 200, sampling distributions for p^ are indeed more bell-shaped when the population proportion p is close to 0.5 than when p is close to zero or one. This is in alignment with the central limit theorem, which states that as the sample size increases, the sampling distribution of the proportion will tend to approximate a normal distribution, especially when p is near 0.5. However, when p is near 0 or 1, the distribution is more skewed and therefore less bell-shaped.
It's also important to note that, according to the empirical rule for bell-shaped distributions, approximately 68 percent of the data falls within one standard deviation of the mean, and approximately 95 percent within two standard deviations, a property that is expected to be true for a well-behaved bell-shaped sampling distribution.