AP Statistics Binomial Normal Quiz – Free PDF

Contents

This ap statistics binomial normal quiz asks 10 multiple-choice questions on binomial and normal distributions, and each answer comes with a short explanation.

Ten multiple-choice questions check the core ideas of binomial and normal distributions: the BINS conditions, binomial probabilities, z-scores, normal areas and when a normal approximation is reasonable. Each question has exactly one correct answer. Work out the answer first, then read the explanation.

AP StatisticsCommon Core: AP Statistics Unit 2 (2026-27)

🎯 Binomial and Normal Distributions – AP Statistics math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Which situation is a binomial setting?

A Counting the number of aces in a 5-card hand dealt from one standard deck

B Counting the number of defective items in a random sample of 20 items from a very large production run, with 4% defective overall

C Counting the number of rolls of a die needed to get the first 3

D Counting the number of heads when a coin is flipped 10 times, where each flip is adjusted to be 5% more likely than the last

Question 2

X is binomial with n = 12 and p = 0.25. What is the standard deviation of X?

A 2.25

B 3

C 0.75

D 1.5

Question 3

X is binomial with n = 4 and p = 0.5. What is P(X = 2)?

A 0.25

B 0.5

C 0.375

D 0.1875

Question 4

The graph shows a binomial distribution with n = 5 and p = 0.5. The highlighted bars are X = 3, 4 and 5. What is P(X ≥ 3)?

Binomial, n = 5, p = 0.5.

A 0.3125

B 0.5

C 0.1875

D 0.8125

Question 5

A student has a z-score of 1.5 on a test with mean 70 and standard deviation 8. What is the score?

A 12

B 62

C 82

D 78

Question 6

For a standard normal variable Z, what is the shaded area, P(Z > 1)?

Standard normal curve.

A 0.1587

B 0.8413

C 0.3174

D 0.6826

Question 7

For which pair of values is the normal approximation to the binomial distribution reasonable?

A n = 40, p = 0.1

B n = 25, p = 0.3

C n = 200, p = 0.04

D n = 100, p = 0.5

Question 8

Scores are approximately normal with mean 500 and standard deviation 100. By the 68-95-99.7 rule, about what percent of scores fall in the shaded region, from 400 to 700?

Shaded from 400 to 700.

A 81.5%

B 95%

C 68%

D 84%

Question 9

A fair-looking spinner lands on red with probability 0.2 on each independent spin. What is the probability of at least one red in 6 spins?

A 0.2621

B 0.7379

C 0.6723

D 0.8000

Question 10

Quiz scores are approximately normal with mean 60 and standard deviation 5. What score is at the 90th percentile?

A 53.6

B 68.2

C 66.4

D 65.0

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Binomial setting: Binary outcomes, Independent trials, Number of trials fixed, Same probability of success (BINS).
For a binomial count: \(\mu=np\) and \(\sigma=\sqrt{np(1-p)}\).
Normal probabilities are areas: standardize with \(z=\frac{x-\mu}{\sigma}\), then use Table A or normalcdf.
Percentiles run backward: \(x=\mu+z\sigma\), with \(z\) from the table or invNorm.
Normal approximation to a binomial needs \(np\ge 10\) and \(n(1-p)\ge 10\).