A teacher surveys a random group of students about their preference for doing classwork online or on paper. 17 students did classwork online, 8 students did classwork on paper. How many students out of 350 will most likely have a preference to do their classwork online?
The correct answer and explanation is:
To find how many students out of 350 will most likely prefer doing their classwork online, we first determine the proportion of students in the survey who chose online classwork.
The total number of surveyed students is:
17+8=2517 + 8 = 25
The proportion of students who prefer online classwork is:
1725=0.68\frac{17}{25} = 0.68
Now, we apply this proportion to the total student population of 350:
0.68×350=2380.68 \times 350 = 238
So, approximately 238 students out of 350 will most likely prefer to do their classwork online.
Explanation
Surveys are used in statistics to predict the preferences or behaviors of a larger population based on a smaller, randomly selected sample. In this case, the teacher surveyed 25 students, and 17 of them (or 68%) preferred doing their classwork online.
To estimate the preference of 350 students, we assume that the sample is representative of the whole group. We use proportional reasoning, which means we scale up the percentage from the sample to the larger group while maintaining the same ratio.
By multiplying the total number of students (350) by the proportion who preferred online classwork (0.68), we estimate that around 238 students will have the same preference.
This approach is an example of statistical inference, where a sample’s data is used to make predictions about a larger population. However, real-world results may vary due to factors like survey bias, sample size limitations, or changing student preferences.
Surveys like this help teachers and schools make informed decisions about instructional methods that best suit students’ needs. If the majority of students prefer online classwork, schools may allocate more resources for digital learning tools.
