8. Sampling Distributions & Confidence Intervals: Proportion

Suppose a simple random sample of 1200 adults is selected from a large population in which the proportion of adults who support a certain policy is $p$. What is the mean of the sampling distribution of the sample proportion $\bar{p}$?

The probability of someone voting for a particular candidate in a two-person election is $45\%$ . Use a normal distribution to approximate the probability that between $62$ and $70$ people out of a sample of $100$ vote for the candidate. 

Why is a sample used more often than a population when estimating a population proportion $p$?

In the context of sampling distributions of sample proportions, $\mathrm{population}\mathrm{parameters}$ are difficult to calculate due to which of the following reasons?

Which of the following statements about sampling distributions for the sample mean is false?

A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that a random sample of $100$ people reveals $60$ people or more preferring Pepsi. 

A previous study found that $80\%$ of people preferred drinking Pepsi over Coca Cola. Use a normal distribution to approximate the probability that, from this same random sample of $100$ people, that between $10$ and $11$ people prefer Coca Cola.