---
title: "AP Statistics Unit 2 Practice Test"
description: "A timed AP Statistics Unit 2 (Probability, Random Variables, and Probability Distributions) practice test in the AP format, drawn from 4,197 multiple-choice questions and 25 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-stats/unit-test/2"
type: "unit-test"
subject: "AP Statistics"
unit: "Unit 2"
---

# AP Statistics Unit 2 Practice Test

## Overview

A timed AP Statistics Unit 2 (Probability, Random Variables, and Probability Distributions) practice test in the AP format, drawn from 4,197 multiple-choice questions and 25 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

- 20 Multiple Choice Questions (43 minutes)
- 1 FRQ – FRQ 1 – Multi-Focus on Practices 1 and 2 (23 minutes)
- 1 FRQ – FRQ 2 – Multi-Focus on Practices 3 and 4 (23 minutes)

## Unit FRQs by Type

- [FRQ 1 – Multi-Focus on Practices 1 and 2](/ap-stats/frq-practice?type=frq-1-multi-focus-on-practices-1-and-2&id=6a67c98f2de38de8e968cdaa): 3 questions
- [FRQ 2 – Multi-Focus on Practices 3 and 4](/ap-stats/frqs/frq-2?unit=2): 12 questions
- [FRQ 4 – Multi-Focus on Practices 2, 3, and 4](/ap-stats/frqs/frq-4?unit=2): 10 questions

## Practice Questions

### Question 1

A manufacturing process produces steel bolts with a mean length of 120 mm. A quality control manager needs to calculate the probability that a randomly selected bolt is shorter than 118 mm using a normal approximation. Which additional piece of information is absolutely necessary to perform this calculation?

- (A) The standard deviation of the bolt lengths
- (B) The total number of bolts produced daily
- (C) The mean length of the bolts in a sample
- (D) The tolerance limits set by the customer

**Answer: (A)** Calculating a z-score requires both the mean and the standard deviation to standardize the value of interest. Without the standard deviation, the spread of the distribution is unknown, making it impossible to determine the probability associated with a specific length.

### Question 2

The daily revenue of a small business has a mean of $$500$$ dollars and a standard deviation of $$50$$ dollars. To calculate the probability that the revenue on a single randomly selected day exceeds $$600$$ dollars using the standard normal table, which condition must be assumed?

- (A) The daily revenue follows a normal distribution
- (B) The sample size of days observed exceeds thirty
- (C) The distribution of daily revenue is skewed right
- (D) The daily revenue values are mutually independent

**Answer: (A)** Calculating probabilities for individual observations using z-scores requires the population distribution to be approximately normal. If the population is not normal, the standard normal table cannot be used to find probabilities for a single data point ($$n=1$$).

### Question 3

A standardized test has a mean score of 500 and a standard deviation of 100. A student wants to determine the percentage of test-takers who scored at least 650. Which calculation approach correctly identifies the information needed to solve this problem?

- (A) Find the area under the normal curve to the right of $$z = 1.5$$
- (B) Find the area under the normal curve to the left of $$z = 1.5$$
- (C) Find the area under the normal curve between $$z = -1.5$$ and $$1.5$$
- (D) Find the area under the normal curve to the right of $$z = -1.5$$

**Answer: (A)** The phrase "at least" indicates a need for the upper tail probability. The z-score is calculated as $$(650 - 500) / 100 = 1.5$$, so the relevant area is the region to the right of this value.

### Question 4

A study reports that the mean commute time for a city is 25 minutes with a standard deviation of 5 minutes. A resident wants to calculate the probability that a single randomly selected commuter takes longer than 40 minutes. Which of the following facts would prevent the use of the normal distribution for this specific calculation?

- (A) The distribution of commute times is heavily skewed to the right
- (B) The sample size used to estimate the mean was only 100 commuters
- (C) The standard deviation of 5 minutes is small compared to the mean
- (D) The mean commute time includes delays from daily traffic accidents

**Answer: (A)** Normal probability calculations for individual observations ($$n=1$$) are invalid if the population distribution is heavily skewed. The normal model requires the population to be symmetric and bell-shaped.

### Question 5

A biologist models the length of a certain fish species using a normal distribution with mean $$\mu = 20$$ cm and standard deviation $$\sigma = 2$$ cm. To find the probability that a fish is shorter than 17 cm, which statement correctly identifies and interprets the z-score needed for this calculation?

- (A) $$z = -1.5$$, indicating the value is 1.5 standard deviations below the mean
- (B) $$z = -1.5$$, indicating the value is 1.5 standard deviations above the mean
- (C) $$z = 1.5$$, indicating the value is 1.5 standard deviations below the mean
- (D) $$z = 1.5$$, indicating the value is 1.5 standard deviations above the mean

**Answer: (A)** The z-score is calculated as $$(17 - 20) / 2 = -1.5$$. The negative sign indicates the value is below the mean, and the magnitude represents the distance in standard deviations.

### Question 6

The lifespan of a battery is normally distributed with a mean of 500 hours and a standard deviation of 25 hours. Which key feature of the data allows a user to estimate that approximately 2.5% of batteries last longer than 550 hours without using a calculator?

- (A) The value 550 is exactly two standard deviations above the mean
- (B) The value 550 is exactly one standard deviation above the mean
- (C) The sample size is large enough to apply the Central Limit Theorem
- (D) The distribution is perfectly symmetric around the median of 500

**Answer: (A)** The Empirical Rule states that 95% of data falls within 2 standard deviations. Since 550 is $$2\sigma$$ above the mean ($$500 + 2(25)$$), the remaining 5% is split between the tails, leaving 2.5% in the upper tail.

### Question 7

A machine fills bags of coffee with a mean weight of 16 ounces and a standard deviation of 0.2 ounces. The weights are normally distributed. Which notation correctly identifies the probability that a randomly selected bag weighs between 15.8 and 16.4 ounces?

- (A) $$P(-1.0 < Z < 2.0)$$ using standard normal values
- (B) $$P(-0.2 < Z < 0.4)$$ using raw deviation values
- (C) $$P(15.8 < Z < 16.4)$$ using raw variable values
- (D) $$P(0.2 < Z < 0.4)$$ using standard error values

**Answer: (A)** Standardizing the values gives $$z_1 = (15.8-16)/0.2 = -1.0$$ and $$z_2 = (16.4-16)/0.2 = 2.0$$. The probability corresponds to the area between these two z-scores.

### Question 8

A manufacturing process produces bolts with lengths that are normally distributed with a mean of $$10$$ mm and a standard deviation of $$0.2$$ mm. Bolts are considered defective if they are shorter than $$9.6$$ mm or longer than $$10.4$$ mm. Based on the empirical rule, which claim about the production quality is best supported?

- (A) Approximately $$5\%$$ of the bolts produced will be considered defective
- (B) Approximately $$2.5\%$$ of the bolts produced will be considered defective
- (C) Approximately $$32\%$$ of the bolts produced will be considered defective
- (D) Approximately $$0.3\%$$ of the bolts produced will be considered defective

**Answer: (A)** Applying the empirical rule to the boundaries $$9.6$$ ($$\mu - 2\sigma$$) and $$10.4$$ ($$\mu + 2\sigma$$) shows that $$95\%$$ of bolts fall within the acceptable range, leaving $$5\%$$ as defective.

### Question 9

A student took two standardized tests. On Test A, the mean was $$500$$ with a standard deviation of $$100$$, and the student scored $$650$$. On Test B, the mean was $$20$$ with a standard deviation of $$5$$, and the student scored $$32$$. Assuming both distributions are normal, which conclusion about the student's performance is most appropriate?

- (A) Performance was stronger on Test B, indicated by a z-score of $$2.4$$ versus $$1.5$$
- (B) Performance was stronger on Test A, indicated by a raw score of $$650$$ versus $$32$$
- (C) Performance was stronger on Test A, indicated by a z-score of $$1.5$$ versus $$2.4$$
- (D) Performance was equal on both tests, indicated by proportional scaling of scores

**Answer: (A)** Calculating the z-scores reveals the student is $$1.5$$ standard deviations above the mean on Test A and $$2.4$$ above on Test B, indicating a relatively higher performance on Test B.

### Question 10

Annual rainfall in a region is normally distributed with a mean of $$40$$ inches and a standard deviation of $$4$$ inches. A drought is defined as a year with less than $$32$$ inches of rain. Based on the empirical rule, which claim about the frequency of droughts is supported?

- (A) Drought conditions are expected to occur in approximately $$2.5\%$$ of years
- (B) Drought conditions are expected to occur in approximately $$5.0\%$$ of years
- (C) Drought conditions are expected to occur in approximately $$16\%$$ of years
- (D) Drought conditions are expected to occur in approximately $$0.15\%$$ of years

**Answer: (A)** Identifying that $$32$$ inches is $$2$$ standard deviations below the mean ($$z = -2$$) leads to the conclusion that the area in the left tail is approximately $$2.5\%$$.

## Review the Unit

- [2.1 Tabular and Graphical Representations for the Distributions of Two Categorical Variables](/ap-stats/unit-2/representing-two-categorical-variables/study-guide/adVExzxFopPqv91AYcgp)
- [2.2 Summary Statistics for Two Categorical Variables](/ap-stats/unit-2/statistics-for-two-categorical-variables/study-guide/0SjltJrb2O0gXsmucKt1)
- [2.3 Estimating Probabilities Using Simulation](/ap-stats/unit-2/estimating-probabilities-using-simulation/study-guide/ABwpnnUf4VCXeVbB9q72)
- [2.4 Introduction to Probability](/ap-stats/unit-2/intro-probability/study-guide/gfnBWfyMANOxF3vWLrbA)
- [2.5 Mutually Exclusive Events](/ap-stats/unit-2/mutually-exclusive-events/study-guide/iBljImMDLJ8bSWeWXbi6)
- [2.6 Conditional Probability](/ap-stats/unit-2/conditional-probability/study-guide/fiabQj72yj93Hti9l8oR)
- [2.7 Independent Events and Unions of Events](/ap-stats/unit-2/independent-events-unions-events/study-guide/aMOuOhtDQIJAtgZx3JNz)
- [2.8 Introduction to Random Variables and Probability Distributions](/ap-stats/unit-2/intro-random-variables-probability-distributions/study-guide/B5MJ1YqQJ4D455wegCvz)
- [2.9 Parameters of Random Variables](/ap-stats/unit-2/mean-standard-deviation-random-variables/study-guide/g1wJm2o6V4wCoqbsC5Px)
- [2.10 The Binomial Distribution](/ap-stats/unit-2/intro-binomial-distribution/study-guide/uvU3qsHmVgEuPjvhgaEC)
- [2.11 The Normal Distribution](/ap-stats/unit-2/normal-distribution-revisited/study-guide/dx4vMcx3WjSw68f1Ov66)
- [2.12 Sampling Distributions and the Central Limit Theorem](/ap-stats/unit-2/central-limit-theorem/study-guide/DPmpebCrsJBYfpSgOKn3)
- [Unit 2 Overview: Probability, Random Variables, and Probability Distributions](/ap-stats/unit-2/review/study-guide/JeaowG56kC80Eu94VWs7)

## Other Unit Tests

- [Unit 1: Exploring One–Variable Data and Collecting Data](/ap-stats/unit-test/1)
- [Unit 3: Inference for Categorical Data: Proportions](/ap-stats/unit-test/3)
- [Unit 4: Inference for Quantitative Data: Means](/ap-stats/unit-test/4)
- [Unit 5: Regression Analysis](/ap-stats/unit-test/5)

## About This Document

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- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
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