A store manager reviewed the receipts from 80 customers who were selected at random from all the customers who made...

1. TRANSLATE the problem information

• Given information:
  • Random sample: 80 customers selected from all Thursday customers
  • Sample result: 20 out of 80 purchased fruit
  • Total Thursday customers: 1,500
  • Need: Most appropriate conclusion about fruit purchases

• What this tells us: We have sample data to estimate population behavior, but cannot determine exact numbers

2. INFER the approach

• This is a statistical sampling problem - we use sample proportions to estimate population totals
• Since it's a random sample, we can only make estimates, not determine exact values
• Strategy: Calculate sample proportion, then scale up to full population

3. SIMPLIFY to find the sample proportion

• Customers who bought fruit in sample: 20 out of 80
• Sample proportion = \(\frac{20}{80}\) = \(\frac{1}{4}\) = \(0.25\)

4. SIMPLIFY to estimate the population total

• Apply sample proportion to full population:
• Estimated fruit buyers = \(\frac{1}{4} \times 1,500\) = \(375\)

5. INFER the correct conclusion type

• Eliminate choices A and B: Use word "exactly" but sampling gives estimates only
• Between C and D: Our calculation gives 375, not 75
• Choice D correctly states this is a "best estimate" of 375

Answer: D. The best estimate for the number of customers who purchased fruit last Thursday is 375.

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread the total population as 300 instead of 1,500, or confuse which numbers to use in their calculation.

They might calculate \(\frac{20}{80} \times 300 = 75\), leading them to select Choice C (75) because they see "best estimate" language and their arithmetic matches.

Second Most Common Error:

Poor INFER reasoning about sampling: Students don't understand the difference between exact values and estimates from sample data.

They perform correct arithmetic to get 375 but select Choice B (Exactly 375 customers must have purchased fruit) because they don't recognize that sampling only provides estimates, never exact population values.

The Bottom Line:

This problem tests whether students understand that random sampling produces estimates of population characteristics, not exact counts, combined with proportional reasoning skills to scale sample results to full populations.