Skip to content
Home › AP Statistics Math › AP Statistics Tests › Binomial and Normal Test – AP Statistics Math (Printable PDF)

Binomial and Normal Test – AP Statistics Math (Printable PDF)

Last updated: October 22, 2026 · Written by the Math Made Easy math teachers

AP Statistics Math Tests – Mathbot, the Math Made Easy robot coach, with free printable tests for AP Statistics
This 45-minute test has eight AP-style questions worth 20 points. Define each variable, show the setup and standardizing steps, and state conclusions in the context of the problem.

Standards: AP Statistics Unit 2 (2026-27) · Level: Grade 12 AP Statistics

Time: 45 minutes · 8 questions · Total: 20 points · Calculator: as allowed by your teacher

Question 1 Binomial Setting (2 points)

A coach records whether each of the 12 players on her team passes a fitness test (each passes independently with probability 0.8). Let X be the number that pass. Check each condition for a binomial setting and state the distribution of X.

Question 2 Binomial Calculations (3 points)

Let X be binomial with n = 10 and p = 0.3. (a) Find P(X = 4). (b) Find P(X ≥ 1). (c) Find the mean and standard deviation of X.

Question 3 Shape and Tail Probability (2 points)

The graph shows the distribution of a binomial variable X with n = 8 and p = 0.2.

0.00.10.20.30.4Probability012345678Number of successes X
Distribution of X.
  1. Describe the shape. (1 point)
  2. Find P(X ≥ 3). (1 point)

Question 4 Normal Probability (2 points)

The time to complete a trail run is approximately normal with mean 250 minutes and standard deviation 30 minutes. Find the probability that a randomly selected runner finishes between 210 and 280 minutes.

Question 5 Percentiles and Unknown Parameters (3 points)

Resting heart rates in a group are approximately normal with mean 68 beats per minute and standard deviation 7.2. (a) Find the 85th percentile. (b) A second group has a normal distribution with mean 70 in which the 20th percentile is 63. Find its standard deviation.

Question 6 Tails of a Normal Model (3 points)

Weights of cereal boxes are approximately normal with mean 500 grams and standard deviation 40 grams. The figure shades the area below 440 grams.

380420440500580620Weight (grams)
Cereal box weights: mean 500 g, standard deviation 40 g.
  1. Find the proportion of boxes below 440 grams. (1 point)
  2. Find the proportion of boxes that weigh more than 580 grams. (1 point)
  3. Find the proportion of boxes that are either below 440 or above 580 grams. (1 point)

Question 7 Normal Approximation (3 points)

A school’s attendance records show that 20% of students are late at least once a week. In a random sample of 300 students, let X be the number who are late at least once. (a) Verify the conditions for a normal approximation. (b) Approximate P(X ≥ 70).

Question 8 Normal Then Binomial (2 points)

The thickness of a machined part is approximately normal with mean 5.15 mm and standard deviation 0.10 mm. A part is rejected if it is thinner than 5.00 mm. Find the probability that a part is rejected, then the probability that at least 1 of 5 independent parts is rejected.

View the Binomial And Normal test answer key with scoring

Binomial And Normal lessonBinomial And Normal worksheetBinomial And Normal quiz

Mis à jour le