According to the U.S. Census Bureau, approximately 45% of the 29 million 18- to 24-year-olds in the United States are enrolled in college. To more accurately gauge these young voters, an Edgewood College, Madison, WI, professor conducted a national college on campus survey of 945 18- to 24-year-olds at 29 colleges in October 19–21, 2004. The survey analyzed which sources of information most influenced students’ votes. Based upon a scale of 0 to 100, with 100 being most influential, students said the top influence was the presidential debates (mean = 69.05, standard deviation = 31.65).
a. According to Chebyshev’s theorem, at least what percent of the scores are between 5.75 and 132.35?
b. If it is known that these scores are normally distributed, what percent of these scores are between 5.75 and 132.35?
c. Explain why the relationship between the interval bounds in parts a and b and the mean and standard deviation given in the question suggest that the distribution of scores is not normally distributed. Include specifics.