Correct Answer: C (5.320)

To find the average height of all the students, we need to calculate the weighted average based on the number of students in each group (female and male).

Step 1: Understand the Weighted Average Formula

The formula for the combined average of two groups is:

$$ \bar{x}_{\text{total}} = \frac{n_f \bar{x}_f + n_m \bar{x}_m}{n_f + n_m} $$

Where:

• $n_f$ = number of female students = 40
• $\bar{x}_f$ = average height of female students = 5.15 feet
• $n_m$ = number of male students = 20
• $\bar{x}_m$ = average height of male students = 5.66 feet

Step 2: Calculate the Total Sum of Heights

First, we find the sum of the heights for each group and then add them together.

• Sum of heights for females: $n_f \times \bar{x}_f = 40 \times 5.15 = 206$ feet
• Sum of heights for males: $n_m \times \bar{x}_m = 20 \times 5.66 = 113.2$ feet
• Total sum of all heights: $206 + 113.2 = 319.2$ feet

Step 3: Calculate the Total Number of Students

Total students = (Number of females) + (Number of males) = $40 + 20 = 60$.

Step 4: Calculate the Combined Average Height

$$ \bar{x}_{\text{total}} = \frac{\text{Total sum of all heights}}{\text{Total number of students}} = \frac{319.2}{60} = 5.32 $$

The average height of all the students in the class is 5.320 feet.