According to the National Center for Education Statistics (www.nces.ed.gov), the amounts of all loans, including Federal Parent PLUS loans, granted to students during the 2007–2008 academic year had a distribution with a mean of $8109.65. Suppose that the standard deviation of this distribution is $2412.
a. Using Chebyshev’s theorem, find at least what percentage of students had 2007–2008 such loans between
i. $2079.65 and $14,139.65
ii. $3285.65 and $12,933.65
*b. Using Chebyshev’s theorem, find the interval that contains the amounts of 2007–2008 such loans for at least 89% of all students.