Why is the standard deviation of the distribution of all such sample proportions?What is the shape of the distribution of all such sample proportions?

Based on research done by the Bradly Corporation, the proportion of Americans that wash their hands after using the restroom is p = 0.66. You plan to take a random sample of 100 students at BYU-Idaho and calculate the proportion of those who wash their hands in your sample. You want to see if the proportion among BYU-Idaho students is different than the national proportion. Use this information to answer the next three questions