Applied math Matrices

Question

Given the matrices below showing grades, marks, and population distribution by class, how many males scored <80%?

 

                 Sr3     Sr4

>90%      [ 8%       7%]               M     F

80-89%  [27%   22%]        Sr3 [72   68]

70-79%  [52%   46%]        Sr4 [64   66]

<70%     [13%   25%]

Answer 1

The first step is to determine what percentage of Sr3 and Sr4 is male. For Sr3 it is 72/(72+68) = 72/140 = 51.4%. For Sr4 it is 64/(64+66) = 64/130 = 49.2%. With the information given, will will have to make the assumption that the male and female students are evenly distributed throughout the grades.

 

For Sr3, 52%+13%, or 65% of students scored a grade of <80%.The total number of students in Sr3 is 140. To find the number of students that scored <80% we multiple 140 by 0.65 and find that 91 students scored less than 80% on the exam. Continuing our assumption that the male/female distribution of the course is the same as the male/female distribution for each score, we find that 51.4% of 91 students is 46.8 male students scoring <80% in Sr3. 

 

For Sr4, 46% + 35%, or 81% of the students scored under 80% on the exam. The total number of students in Sr4 is 130. 80% of 130 students is  130*0.80=104 students. Again, assuming the same male/female distribution throughout, we find that 49.2% of 104 students is  51.2 male students scoring less than 8% on Sr4.

 

Hope this helps Amy!