Question
In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?
- 16,200
- 23,400
- 30,600
- 46,800
The correct answer is: 30,600
- We have given that 34.6% of 26 students in Mr. Camp’s class reported that they had at least two siblings.
34.6% of 26 = 8.996=9
there must have been 9 students in the class who reported having at least two siblings and remaining 26- 9 = 17 students who reported that they had fewer than two siblings.
- It is also given that the average eighth-grade class size in the state is 26 and that Mr. Camp’s class is representative of all eighth-grade classes in the state. This means that in each eighth-grade class in the state there are about 17 students who have fewer than two siblings. Therefore, the best estimate of the number of eighth-grade students in the state who have fewer than two siblings is
17 × (number of eighth-grade classes in the state),
or 17 × 1,800 = 30,600.
- Option A is incorrect because 16,200 is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings.
Option B is incorrect because 23,400 is half of the estimated total number of eighth-grade students in the state; however, since the students in Mr. Camp’s class are representative of students in the eighth grade classes in the state and more than half of the students in Mr. Camp’s class have fewer than two
- siblings, more than half of the students in each eighth-grade class in the state have fewer than two siblings, too.
- Option D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.
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