Every exam has 100 points. Student's average of 3 exams is 88 points and standard deviation is 3. How many points should he get on fourth and fifth exam so that average is 90 and standard deviation stays same (=3).
I tried solving equations $(x_1+x_2+x_3)/3=88$ and $(x_1+x_2+x_3+x_4+x_5)/5=90$. Since $x_1+x_2+x_3=264$ it means that $(264+x_4+x_5)/5=90$ so $x_4+x_5=186$. Then I tried to use equations for standard deviation but I haven't managed to get anything useful.