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the central limit theorem and unbiased estimators

Review the central limit theorem and unbiased estimators for AP Statistics and try 2 free AP-style practice questions. 19 questions on this topic in AP Statistics · Unit 5 · Sampling Distributions.

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Question 1

A wildlife biologist measured the wingspan of each of 85 randomly selected California condors from a breeding population of 537 birds. The median wingspan of the sampled birds was 108 centimeters. From long-term records, the standard deviation of wingspan for the whole breeding population is 14 centimeters. Which of the following correctly classifies these two numbers?

Question 2

A polling organization will compare the proportion of adults in two cities who support a new transit levy by taking an independent random sample from each city. Before using a normal model for the difference p^1−p^2\hat{p}_1 - \hat{p}_2 between the two sample proportions, the organization must check the large-counts condition. Under which of the following conditions is the sampling distribution of p^1−p^2\hat{p}_1 - \hat{p}_2 approximately normal?

17 more questions on this topic

Full practice for AP Statistics · Unit 5 · Sampling Distributions: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts
Part a1 / 1 pts
Point 1: Earned
Grader confidence 94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts
Point 1: Earned
Grader confidence 91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned
Grader confidence 88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned
Grader confidence 82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

The central limit theorem and unbiased estimators: AP Statistics Practice Questions | S&D Academy