Question

Students took two parts of a test, each worth 50 points. Part A has a variance of 25, and Part B has a variance of 36. The correlation between the test scores is 0.8. (a) If the teacher adds the grades of the two parts together to form a final test grade, what would the variance of the final test grades be? (b) What would the variance of Part A - Part B be?

Answer 1

Answer:

Following are the solution to the given choices:

Step-by-step explanation:

In point a:

Calculating the variance of the test grade:

$\to var(A+B)=var A + var B + 2 cov(A,B)$

                       $=25+36+2(0.8)\\\\=25+36+1.6\\\\=62.6$

In point b:

$\to var(A-B)=varA + var B - 2 cov(A,B)$

                       $=25+36-2(0.8)\\\\=25+36-1.6\\\\=59.4$

The relationship between the top 20 students is also slight, so the top 20 students are more university-like than all secondary students.