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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Evaluating and Inference Sample Statistics

Grade: 1400-a Lesson: S4-L4

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	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 whohave fewer than two siblings?
2	Step	Calculate the total number of eighth-grade students in the state: → There are 1,800 eighth-grade classes in the state. → The average class size is 26 students. → Total number of eighth-grade students = \$1,800 times 26 = 46,800\$.
3	Step	Determine the proportion of students who have fewer than two siblings: → In Mr. Camp’s class, 34.6% of the students reported having at least two siblings. → Therefore, the percentage of students who have fewer than two siblings is: 100% − 34.6% = 65.4%
4	Step	Calculate the number of students who have fewer than two siblings: → The proportion of students with fewer than two siblings is 65.4%. → Apply this proportion to the total number of eighth-grade students: Number of students with fewer than two siblings = 65.4% × 46,800. → Convert the percentage to a decimal for the calculation: 65.4% = 0.654.
5	Step	Number of students with fewer than two siblings = 0.654 × 46,800 Number of students with fewer than two siblings = 30,607.2.
6	Step	We need to choose the closest estimate from the given options so the best estimate is 30,600.
7	Choice.A	This number is significantly lower than our calculation of 30,607.2. It represents only about 34.6% of the total students, which would be the percentage of students with at least two siblings, not fewer than two siblings	16,200
8	Choice.B	This number is closer to the middle but still considerably lower than our calculated result. It does not align with our calculation based on 65.4% of the total students	23,400
9	Choice.C	This is very close to our calculated number of 30,607.2, making it the most accurate and plausible estimate	30,600
10	Choice.D	This option would imply that all students have fewer than two siblings, which contradicts the information that 34.6% have at least two siblings	46,800
11	Answer	Option	C
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

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 whohave fewer than two siblings?

Step

Calculate the total number of eighth-grade students in the state:
→ There are 1,800 eighth-grade classes in the state.
→ The average class size is 26 students.
→ Total number of eighth-grade students = \$1,800 times 26 = 46,800\$.

Step

Determine the proportion of students who have fewer than two siblings:
→ In Mr. Camp’s class, 34.6% of the students reported having at least two siblings.
→ Therefore, the percentage of students who have fewer than two siblings is:
100% − 34.6% = 65.4%

Step

Calculate the number of students who have fewer than two siblings:
→ The proportion of students with fewer than two siblings is 65.4%.
→ Apply this proportion to the total number of eighth-grade students:
Number of students with fewer than two siblings = 65.4% × 46,800.
→ Convert the percentage to a decimal for the calculation: 65.4% = 0.654.

Step

Number of students with fewer than two siblings = 0.654 × 46,800
Number of students with fewer than two siblings = 30,607.2.

Step

We need to choose the closest estimate from the given options so the best estimate is 30,600.

Choice.A

This number is significantly lower than our calculation of 30,607.2. It represents only about 34.6% of the total students, which would be the percentage of students with at least two siblings, not fewer than two siblings

16,200

Choice.B

This number is closer to the middle but still considerably lower than our calculated result. It does not align with our calculation based on 65.4% of the total students

23,400

Choice.C

This is very close to our calculated number of 30,607.2, making it the most accurate and plausible estimate

30,600

Choice.D

This option would imply that all students have fewer than two siblings, which contradicts the information that 34.6% have at least two siblings

46,800

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?