AP Statistics Binomial and Geometric Distributions Test with Point Values (PDF)

AP Statistics math test: Binomial and Geometric Distributions – Maths PDF

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This binomial geometric test for AP Statistics covers binomial and geometric distributions (Common Core AP STAT 4.10, AP STAT 4.11, AP STAT 4.12, HSS-MD.A.3, HSS-CP.B.9), with a free PDF to print.

This 45-minute test covers the binomial and geometric settings, probabilities, means, and standard deviations. State the distribution and its parameters before every calculation.

Time and points

About this test

Grade: AP Statistics
Chapter: Binomial and Geometric Distributions
Standards: AP STAT 4.10, AP STAT 4.11, AP STAT 4.12, HSS-MD.A.3, HSS-CP.B.9
Time: 45 minutes
Total: 20 points

Binomial geometric test: questions

Question 1 – Binomial probability [4 pts]

Binomial with n = 6 and p = 0.4.

X is the number of successes in 6 trials with p = 0.4. (a) Find P(X = 2). (1 point) (b) Find P(X >= 4). (2 points) (c) Find the mean. (1 point)

Question 2 – BINS [3 pts]

A basketball player takes 15 shots, each with probability 0.45 of success. (a) Explain why X, the number made, is binomial by checking all BINS conditions. (2 points) (b) Find P(X = 7). (1 point)

Question 3 – Mean and sd [2 pts]

A multiple-choice quiz has 20 questions with 5 options each. A student guesses on every question. Find the mean and standard deviation of the number correct.

Question 4 – Geometric [3 pts]

Geometric with p = 0.3.

Each game of a carnival has a 30% chance of winning a prize. (a) Find the probability that the first win is on the 3rd game. (1 point) (b) Find the probability that more than 4 games are needed. (1 point) (c) Find the expected number of games. (1 point)

Question 5 – Unusual outcome [2 pts]

A drug works for 85% of patients. In a sample of 20 patients, only 12 improved. Compute P(X <= 12) and decide whether this result is unusual if the 85% claim is true.

Question 6 – Fixed number [1 pt]

BINS check.

Which BINS condition fails when cards are drawn from a deck until an ace appears?

Question 7 – Choose the model [2 pts]

For each situation, name the distribution (binomial or geometric) and its parameters: (a) The number of 6s in 12 rolls of a die. (b) The number of rolls until the first 6.

Question 8 – 10 percent condition [3 pts]

A bag of 40 marbles has 10 red. Five marbles are drawn without replacement. (a) Can the number of red marbles be modeled as binomial? Explain. (2 points) (b) Give a rough probability of exactly 2 red using a binomial model with p = 0.25. (1 point)

Key facts behind this binomial geometric test

Key facts

Binomial conditions: Binary, Independent, fixed Number, Same probability.
Binomial: mean = np, standard deviation = sqrt(np(1-p)); use binompdf and binomcdf.
At least k successes: 1 – binomcdf(n, p, k – 1).
Geometric: trials until the first success; P(X = n) = (1-p)^(n-1) p; mean 1/p.
Without replacement, treat trials as independent only if n is at most 10% of the population.

How to use this binomial geometric test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All AP Statistics chapters: AP Statistics math.

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