To estimate the number of students in the entire school who prefer orange sherbet, we can use the proportion of survey respondents who preferred orange sherbet and apply it to the total student population.
First, we find the proportion of students who prefer orange sherbet based on the survey:
\[ \text{Proportion of orange sherbet lovers} = \frac{\text{Number of students who prefer orange sherbet}}{\text{Total number of surveyed students}} = \frac{10}{130} \]
Now, we calculate this proportion:
\[ \frac{10}{130} = \frac{1}{13} \approx 0.0769 \]
Next, we use this proportion to estimate the total number of students who prefer orange sherbet in the entire school:
\[ \text{Estimated number of students who prefer orange sherbet} = \text{Total number of students} \times \text{Proportion of orange sherbet lovers} \]
Substituting the values:
\[ \text{Estimated number} = 528 \times \frac{10}{130} \]
Calculating that:
\[ 528 \times \frac{10}{130} = 528 \times 0.0769 \approx 40.8 \]
Rounding to the nearest whole number, we find that approximately 41 students in the school prefer orange sherbet.
Thus, the correct answer is:
41