Let X be a binomial random variable with a fixed probability of success on each trial. Which of the following best describes how the shape of the distribution of X changes as the number of trials increases?
the binomial and geometric distributions
Review the binomial and geometric distributions for AP Statistics and try 2 free AP-style practice questions. 12 questions on this topic in AP Statistics · Unit 2 · Probability, Random Variables, and Probability Distributions.
9 topics124 multiple-choice8 free-response
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A call centre places calls one after another, and each call independently results in a sale with probability 0.1. A supervisor records the number of calls needed, up to and including the first call that results in a sale. Which of the following is the expected number of calls?
Sample free-response question
A basketball player makes 50 percent of her shots, and shots are independent. In one game she made 7 shots in a row. Her coach simulates 10 shots many times to see how often a run of 7 or more makes happens.
(a) Describe how to use random digits to simulate one trial of 10 shots.
(b) In 500 simulated trials, a run of 7 or more makes happened 14 times. Estimate the probability and interpret it.
(c) Does the simulation suggest the player's streak is unusual for a 50% shooter? Explain.
(d) How would the estimate change if the coach ran 5,000 trials instead of 500? Explain.
(e) Identify one assumption of the simulation that might not hold in a real game.
10 more questions on this topic
Full practice for AP Statistics · Unit 2 · Probability, Random Variables, and Probability 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% sureReason: 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% sureReason: Graph shows relatively inelastic demand.
Evidence: Draws a steep demand curve.
Point 2: Earned
Grader confidence 88% sureReason: Correct new equilibrium price.
Evidence: Shifts supply left, P1 → P2.
Point 3: Not earned
Grader confidence 82% sureReason: With inelastic demand, a price increase raises total revenue.
Evidence: "Revenue goes down."