Jackie S. answered • 12/20/19

Masters in statistics and 10+ years of experience in academia

We have four total groups, namely, students who:

(a) complete math homework regularly and have a B or higher in the class,

(b) complete math homework regularly and do not have a B or higher in the class,

(c) do not complete math homework regularly but have a B or higher in the class,

(d) do not complete math homework regularly and do not have a B or higher in the class.

For easier calculations, let's assume that there are 100 total students. Since 40% of students are in group (d), we know that there are 40 students in group (d), which means that there are 100 - 40 = 60 students in groups (a), (b) and (c) combined.

Let's let x be the number of students in group (a). Then we know that

x + (48 - x) + (55 - x) = 60.

Why? Well, we know that 48% of students, or 48 students, complete homework regularly, so if there are x students who complete homework regularly and have a B or higher, there are 48 - x students who complete homework regularly and do not have a B or higher.

Similarly, we know that 55% of students, or 55 students, have a B or higher, so if x students have a B or higher and complete their homework regularly, then 55 - x have a B or higher but do not complete their homework regularly.

So let's solve for x:

x + (48 - x) + (55 - x) = 60, so

103 - x = 60 and therefore x = 103 - 60 = 43.

Then we know that there are 43 students in group (a), 48 - 43 = 5 students in group (b), 55 - 43 = 12 students in group (c) and 40 students in group (d).

The total number of students who complete their homework regularly is the number of students in groups (a) or (b), or 43 + 5 = 48. And the number of students who do not complete their homework regularly is the number of students in groups (c) or (d), or 12 + 40 = 52.

Among the 48 students who complete their homework regularly, 43 have a B or higher, so 43/48 or approximately 89.6% of students who complete their homework regularly have a B or higher.

Among the 52 students who do not complete their homework regularly, 12 have a B or higher, so 12/52 or approximately 23.1% of students who do not complete their homework regularly have a B or higher.

So 89.6% of students who complete their homework have a B or higher and only 23.1% of students who don't complete their homework regularly have a B or higher, which supports the teacher's claim.