There are 55 students in Spanish club. A sample of the Spanish club students was selected at random and asked...

1. TRANSLATE the problem information

• Given information:
  • Total Spanish club students: 55
  • Sample result: 20% intend to enroll in the study program
• What we need to find: Total number of Spanish club students who intend to enroll

2. INFER the estimation approach

• The key insight: When we survey a sample and find that 20% intend to enroll, we use this as our best estimate for the entire population
• Strategy: Apply the sample percentage (20%) to the total population (55 students)

3. TRANSLATE percentage to calculation

• Convert percentage to decimal: \(20\% = 0.20\)
• Set up the calculation: \(0.20 \times 55\)

4. Calculate the result

\(0.20 \times 55 = 11\) students

Answer: A. 11

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse what the 20% represents, thinking it's the actual number of students rather than a proportion to be applied to the total population.

They might see "20%" and immediately look for answer choice B (20), not realizing they need to calculate 20% OF the 55 total students. This leads them to select Choice B (20).

Second Most Common Error:

Incomplete INFER reasoning: Students understand they need to do a calculation but get confused about which numbers to work with, potentially calculating the students who DON'T intend to enroll instead.

They might calculate \(80\%\) of \(55\) (the students who don't intend to enroll) and get 44, leading them to select Choice C (44).

The Bottom Line:

This problem requires understanding the connection between sample data and population estimates - the sample gives us a percentage that we then apply to find the actual number in the full population.