In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and percent of the students reported that they had at least two siblings.The average eighth‑grade class size in the state is . If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 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?
It is given that of students in Mr. Camp’s class reported that they had at least two siblings. Since of is , there must have been students in the class who reported having at least two siblings and 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 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 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 Choice A is incorrect because is the best estimate for the number of eighth-grade students in the state who have at least, not fewer than, two siblings. Choice B is incorrect because 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. Choice D is incorrect because 46,800 is the estimated total number of eighth-grade students in the state.