Question

98. A class of 20 students has a mean grade of 80 on a test. Nineteen of the students has a mean grade between 79 and 82, inclusive.

a. What is the lowest possible grade of the other student?

b. What is the highest possible grade of the other student?

Answer 1

$Let~x_i=grade~of~ith~student,~i=1(1)19~and~assume~x_{20}~be~the~grade\\ ~of~other~student.\\ then~79\leq \frac{x_1+x_2+...+x_{19}}{19}\leq 82\\ or,~79*19\leq \sum_{i=1}^{20} x_i-x_{20}\leq 82*19\\ or,~1501\leq 80*20-x_{20}\leq 1558,~since~\bar{x}=\frac{1}{20}\sum_{i=1}^{20}x_i=80\\ or,~1501-1600\leq -x_{20}\leq 1558-1600\\ or,~42\leq x_{20}\leq 99\\ a.~Answer~of~a.~is~42.\\ b.~Answer~of~b.~is~99.$