Question

members of the student government are planning a movie night on campus. they have asked a random sample of students which of four movies the students would prefer. here are the results.

there are 800 students total on campus.

based on the above information, how many students on campus would we expect to prefer movie d? round your answer to the nearest whole number. do not round any intermediate calculations.

Explanation:

Step1: Calculate total sample size

First, find the total number of students in the sample by adding the number of students who preferred each movie.
$19 + 24 + 23 + 54 = 120$

Step2: Find the proportion of students who preferred Movie D in the sample

The proportion of students who preferred Movie D in the sample is the number of students who preferred Movie D divided by the total sample size.
$\frac{54}{120}$

Step3: Multiply the proportion by the total number of students on campus

To find the expected number of students who prefer Movie D on campus, multiply the proportion from Step 2 by the total number of students (800).
$800\times\frac{54}{120} = 800\times0.45 = 360$

Answer:

360