On a recent quiz about averages, the following information is known:• There were three questions on the quiz.• Each question was worth 1 mark.• Each question was marked either right or wrong (no part marks).• 50% of the students got all 3 questions correct.• 5% of the students got no question correct.• The class average mark was 2.3 out of 3.Determine the percentage of students who got exactly 1 question correct and thepercentage of students who got exactly 2 questions correct.

To solve this problem, we first need to understand that the total percentage of students is 100%.

We know that 50% of students got all 3 questions correct and 5% of students got no question correct. This means that the remaining students either got 1 or 2 questions correct.

So, we subtract the percentage of students who got all questions correct and who got no question correct from the total percentage:

100% - 50% - 5% = 45%

This 45% represents the students who got either 1 or 2 questions correct.

Next, we need to use the information about the class average mark. The average mark was 2.3 out of 3. This means that, on average, students got 2.3 questions correct.

We can set up the following equation to represent this information:

(3 * 0.50) + (2 * x) + (1 * y) = 2.3

where x is the percentage of students who got exactly 2 questions correct and y is the percentage of students who got exactly 1 question correct.

We also know that x + y = 0.45 (from the 45% we calculated earlier).

Now we have a system of two equations, and we can solve for x and y:

From the second equation, we can express y as y = 0.45 - x.

Substitute y in the first equation:

(3 * 0.50) + (2 * x) + (1 * (0.45 - x)) = 2.3

Solving this equation gives x = 0.35, or 35%.

Substitute x = 0.35 in the equation y = 0.45 - x gives y = 0.10, or 10%.

So, 35% of students got exactly 2 questions correct and 10% of students got exactly 1 question correct.