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Population Inferences

Grade 7 · Statistics · Worksheet 2

  1. Charlotte surveys a random sample of 150 students at her school and finds that 96 of them prefer pizza over tacos for lunch. If the school has 1,250 students, estimate the number of students who prefer pizza over tacos. Answer: ______________
  2. A random sample of 240 students from a large school shows that 156 students prefer digital textbooks over printed ones. Based on this sample, what is the estimated number of students in the entire school of 1200 students who prefer digital textbooks? Answer: ______________
  3. (-4)³ + 2 × (18 - 5)² ÷ 13 = ? Answer: ______________
  4. A random sample of 200 students at a school shows that 85 prefer year-round school. If the school has 1200 students, estimate how many students in the entire school prefer year-round school. Answer: ______________
  5. A wildlife biologist is studying the population of gray wolves in a national park. She uses a capture-recapture method where she first tags 180 wolves. Two months later, she captures 250 wolves and finds that 45 of them have tags. Based on this data, what is the estimated total wolf population in the park? Answer: ______________
  6. A random sample of 72 students from a middle school shows that 27 prefer online homework. Estimate how many students in the entire school of 672 students prefer online homework. Answer: ______________
  7. A random sample of 75 students from a school of 1200 students shows that 45 prefer online learning. Estimate the number of students in the entire school who prefer online learning. Answer: ______________
  8. Emma surveys a random sample of 80 students at her school. 55 of them say they prefer pizza over burgers. If the school has 1200 students, estimate how many students in the entire school prefer pizza over burgers. Answer: ______________
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Answer Key & Explanations

Population Inferences · Grade 7 · Worksheet 2

  1. Charlotte surveys a random sample of 150 students at her school and finds that 96 of them prefer pizza over tacos for lunch. If the school has 1,250 students, estimate the number of students who prefer pizza over tacos. Answer: 800 Solution: Find the proportion of students in the sample who prefer pizza: 96 out of 150, or 96/150. Simplify the fraction: 96/150 = 16/25 (divide numerator and denominator by 6).
    Full step-by-step solution

    Step 1: Find the proportion of students in the sample who prefer pizza: 96 out of 150, or 96/150. Step 2: Simplify the fraction: 96/150 = 16/25 (divide numerator and denominator by 6). Step 3: Use this proportion to estimate for the whole school: (16/25) × 1,250. Step 4: Multiply: 16 × (1,250 ÷ 25) = 16 × 50 = 800. The answer is 800.

  2. A random sample of 240 students from a large school shows that 156 students prefer digital textbooks over printed ones. Based on this sample, what is the estimated number of students in the entire school of 1200 students who prefer digital textbooks? Answer: 780 Solution: Find the proportion from the sample: 156 out of 240 students prefer digital textbooks. Proportion = 156/240 = 0.65. Apply this proportion to the total school population: 0.65 × 1200 = 780.
    Full step-by-step solution

    Step 1: Find the proportion from the sample: 156 out of 240 students prefer digital textbooks. Proportion = 156/240 = 0.65. Step 2: Apply this proportion to the total school population: 0.65 × 1200 = 780. The estimated number of students who prefer digital textbooks in the entire school is 780.

  3. (-4)³ + 2 × (18 - 5)² ÷ 13 = ? Answer: -38 Solution: Calculate the exponent (-4)³ = -4 × -4 × -4 = 16 × -4 = -64 Calculate inside the parentheses (18 - 5) = 13 Calculate the exponent 13² = 169 Multiply 2 × 169 = 338 Divide 338 ÷ 13 = 26 Add the results: -64 + 26 = -38 The answer is -38.
    Full step-by-step solution

    Step 1: Calculate the exponent (-4)³ = -4 × -4 × -4 = 16 × -4 = -64 Step 2: Calculate inside the parentheses (18 - 5) = 13 Step 3: Calculate the exponent 13² = 169 Step 4: Multiply 2 × 169 = 338 Step 5: Divide 338 ÷ 13 = 26 Step 6: Add the results: -64 + 26 = -38 The answer is -38.

  4. A random sample of 200 students at a school shows that 85 prefer year-round school. If the school has 1200 students, estimate how many students in the entire school prefer year-round school. Answer: 510 Solution: Find the proportion of students in the sample who prefer year-round school: 85 out of 200. Write as a fraction: 85/200. Simplify the fraction: 85/200 = 17/40 (divide numerator and denominator by 5).
    Full step-by-step solution

    Step 1: Find the proportion of students in the sample who prefer year-round school: 85 out of 200. Write as a fraction: 85/200. Step 2: Simplify the fraction: 85/200 = 17/40 (divide numerator and denominator by 5). Step 3: Use this proportion to estimate for the entire school of 1200 students: (17/40) × 1200. Step 4: Multiply: 17 × 1200 = 20400, then divide by 40: 20400 ÷ 40 = 510. The answer is 510.

  5. A wildlife biologist is studying the population of gray wolves in a national park. She uses a capture-recapture method where she first tags 180 wolves. Two months later, she captures 250 wolves and finds that 45 of them have tags. Based on this data, what is the estimated total wolf population in the park? Answer: 1000 Solution: Set up the proportion for capture-recapture method Number initially tagged = 180 Number in second sample = 250 Number tagged in second sample = 45 The proportion should be: (tagged in second sample)/(total in second sample) = (total tagged)/(total population) 45/250 = 180/N 45 × N = 180 × 250…
    Full step-by-step solution

    Step 1: Set up the proportion for capture-recapture method Let N be the total population Number initially tagged = 180 Number in second sample = 250 Number tagged in second sample = 45 Step 2: The proportion should be: (tagged in second sample)/(total in second sample) = (total tagged)/(total population) 45/250 = 180/N Step 3: Cross-multiply to solve for N 45 × N = 180 × 250 45N = 45,000 Step 4: Divide both sides by 45 N = 45,000 ÷ 45 N = 1,000 The estimated total wolf population is 1,000.

  6. A random sample of 72 students from a middle school shows that 27 prefer online homework. Estimate how many students in the entire school of 672 students prefer online homework. Answer: 252 Solution: Find the proportion of students in the sample who prefer online homework: 27 out of 72 = 27/72 = 3/8 (simplify by dividing numerator and denominator by 9).
    Full step-by-step solution

    Step 1: Find the proportion of students in the sample who prefer online homework: 27 out of 72 = 27/72 = 3/8 (simplify by dividing numerator and denominator by 9). Step 2: Use this proportion to estimate for the entire school: (3/8) × 672 = (3 × 672) ÷ 8 = 2016 ÷ 8 = 252. Step 3: So, we estimate that 252 students in the entire school prefer online homework. The answer is 252.

  7. A random sample of 75 students from a school of 1200 students shows that 45 prefer online learning. Estimate the number of students in the entire school who prefer online learning. Answer: 720 Solution: Find the proportion of students in the sample who prefer online learning: 45 out of 75 = 45/75 = 3/5 = 0.6. Apply this proportion to the total school population: 0.6 × 1200 = 720.
    Full step-by-step solution

    Step 1: Find the proportion of students in the sample who prefer online learning: 45 out of 75 = 45/75 = 3/5 = 0.6. Step 2: Apply this proportion to the total school population: 0.6 × 1200 = 720. Step 3: Therefore, we estimate that 720 students in the entire school prefer online learning. The answer is 720.

  8. Emma surveys a random sample of 80 students at her school. 55 of them say they prefer pizza over burgers. If the school has 1200 students, estimate how many students in the entire school prefer pizza over burgers. Answer: 825 Solution: Find the proportion of students in the sample who prefer pizza: 55 out of 80 = 55/80 = 11/16 = 0.6875. Multiply this proportion by the total school population: 0.6875 × 1200 = 825.
    Full step-by-step solution

    Step 1: Find the proportion of students in the sample who prefer pizza: 55 out of 80 = 55/80 = 11/16 = 0.6875. Step 2: Multiply this proportion by the total school population: 0.6875 × 1200 = 825. Step 3: So, we estimate that about 825 students in the entire school prefer pizza over burgers. The answer is 825.