Question

The following table shows the data collected from a random sample of 100 middle school students on the number of hours they play outdoor games every week:

Weekly Duration of Outdoor Games

Time (in hours) 0–2 3–5 6–8 9–11
Number of Students 30 62 8 0

There are 1,200 students in the school. Based on the sample proportion, how many students in the school would be expected to play outdoor games for at least three hours every week?
744

840

960

1,104

Answer 1

[AI-generated answer — Explain Bot]

To determine the number of students in the school who would be expected to play outdoor games for at least three hours every week, we need to calculate the sample proportion and then apply it to the total number of students in the school.

First, let's calculate the sample proportion of students who play outdoor games for at least three hours every week. The sample proportion is calculated by dividing the number of students in the sample who play outdoor games for at least three hours (which is the sum of students in the "3–5", "6–8", and "9–11" categories) by the total number of students in the sample.

Number of students playing outdoor games for at least three hours = 62 (students in the "3–5" category) + 8 (students in the "6–8" category) + 0 (students in the "9–11" category) = 70

Sample proportion = Number of students playing outdoor games for at least three hours / Total number of students in the sample = 70 / 100 = 0.7

Next, we apply this sample proportion to the total number of students in the school to find the number of students who would be expected to play outdoor games for at least three hours every week.

Number of students in the school = 1,200

Expected number of students playing outdoor games for at least three hours = Sample proportion * Number of students in the school = 0.7 * 1200 = 840

Therefore, based on the sample proportion, we can expect 840 students in the school to play outdoor games for at least three hours every week.

So, the correct answer is 840.