In order to estimate the number of students that prefer movie D, first let's calculate the sample size of the research:
[tex]20+21+34+50=125[/tex]
Then, we can use the following rule of three:
[tex]\begin{gathered} students\rightarrow movie\text{ D} \\ 125\rightarrow50 \\ 800\rightarrow x \end{gathered}[/tex]
Now, we can write the following proportion and solve it for x:
[tex]\begin{gathered} \frac{125}{800}=\frac{50}{x}\\ \\ x\cdot125=800\cdot50\\ \\ x=\frac{800\cdot50}{125}\\ \\ x=320\text{ students} \end{gathered}[/tex]
Therefore the answer is 320 students.
