Problem 12

Explanation

Let:

• $\bar{x}_K =$ Class average score
• $n_L =$ Number of male students
• $n_P =$ Number of female students
• $\bar{x}_L =$ Average score of male students
• $\bar{x}_P =$ Average score of female students

Given:

• $\bar{x}_K = 7.5$
• $\frac{n_L}{n_P} = \frac{3}{4} \implies n_L = 0.75 n_P$
• $\bar{x}_P = 1.75 + \bar{x}_L$

The class average score can be obtained as follows:

Substitute the known values:

Therefore, the average score of female students is: