Option 'b' is correct.
Step-by-step explanation:
Since we have given that
Average marks in Homework = 95
Average marks in Quiz = 90
Average marks in Test = 87
According to question, we have that the teacher weights homework at 20%, Quizzes at 20%, Test at 40%, and the final exam at 20%
Total score in the class = 90
So, Score of homework is given by
![0.2\times 95\\\\=19](/tpl/images/0229/0915/a37ab.png)
Score of Quiz is given by
![0.2\times 90\\\\=18](/tpl/images/0229/0915/6b831.png)
Score of test is given by
![0.4\times 87\\\\=34.8](/tpl/images/0229/0915/a5cf9.png)
So, it becomes,
![19+18+34.8+x=90\\\\71.8+x=90\\\\x=90-71.8\\\\x=18.2](/tpl/images/0229/0915/45aa9.png)
So, minimum grade Anna can make on the final is given by
![\dfrac{20}{100}\times y=18.2\\\\y=\dfrac{18.2}{0.2}\\\\y=91](/tpl/images/0229/0915/eb28b.png)
Hence, Option 'b' is correct.