The College Board’s Annual Survey of Colleges provides up-to-date information on tuition and other expenses associated with attending public and private nonprofit institutions of postsecondary education in the United States. Each fall, the College Board releases the survey results on how much colleges and universities are charging undergraduate students in the new academic year. The survey indicated that the average published tuition and fees for 2005–2006 were $8,244 at public four-year colleges and universities and $28,500 at private, nonprofit four-year colleges and universities. The standard deviation was approximately $4,500 at public four-year colleges and universities and approximately $12,000 for private colleges and universities.
a. Do the private, nonprofit four-year colleges and universities have the larger relative variability? Provide statistical evidence to support your answer.
b. If the data on published tuition and fees were bell shaped, determine the largest and smallest amount paid at the four-year private, nonprofit colleges and universities.
c. Based on your answer to part b, do you believe that the data are bell shaped? Support your answer using statistical reasoning.