Question

Each​ fall, a certain organization releases 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 a certain academic year were ​$ 9 comma 310 9,310 at public​ four-year colleges and universities and ​$ 32 comma 315 32,315 at​ private, nonprofit​ four-year colleges and universities. Assume that the standard deviation was approximately ​$ 4 comma 250 4,250 at public​ four-year colleges and universities and approximately ​$ 12 comma 150 12,150 for private colleges and universities. Complete parts a and b. a/ Do the​ private, nonprofit​ four-year colleges and universities have the larger relative​ variability? Select the correct choice below and fill in the answer box to complete your choice 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.

Answer 1

a.

Coefficient of variation for public colleges =

= (4250 / 9310) * 100

= 45.65%

Coefficient of variation for private colleges =

= (12150 / 32315) * 100

= 37.60%

Since, Coefficient of variation for private colleges is less than Coefficient of variation for public colleges, the the​ private, nonprofit​ four-year colleges and universities do not have the larger relative​ variability.

b)

By Empirical rule, virtually all of the data are contained within 3 standard deviations.

Largest amount paid at the​ four-year private =   = 32315 + 3 * 12150 = 68765

Smallest amount paid at the​ four-year private =   = 32315 - 3 * 12150 = -4135

Since, the amount cannot be negative, the Smallest amount paid at the​ four-year private is 0.