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AP Statistics Unit 2 practice questions

Try 10 multiple-choice questions from Unit 2 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

  1. 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?

    The standard deviation of the bolt lengths

    The total number of bolts produced daily

    The mean length of the bolts in a sample

    The tolerance limits set by the customer

    Show answer

    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.

  2. Question 2

    The daily revenue of a small business has a mean of 500500 dollars and a standard deviation of 5050 dollars. To calculate the probability that the revenue on a single randomly selected day exceeds 600600 dollars using the standard normal table, which condition must be assumed?

    The daily revenue follows a normal distribution

    The sample size of days observed exceeds thirty

    The distribution of daily revenue is skewed right

    The daily revenue values are mutually independent

    Show answer

    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=1n=1).

  3. 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?

    Find the area under the normal curve to the right of z=1.5z = 1.5

    Find the area under the normal curve to the left of z=1.5z = 1.5

    Find the area under the normal curve between z=−1.5z = -1.5 and 1.51.5

    Find the area under the normal curve to the right of z=−1.5z = -1.5

    Show answer

    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(650 - 500) / 100 = 1.5, so the relevant area is the region to the right of this value.

  4. 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?

    The distribution of commute times is heavily skewed to the right

    The sample size used to estimate the mean was only 100 commuters

    The standard deviation of 5 minutes is small compared to the mean

    The mean commute time includes delays from daily traffic accidents

    Show answer

    Answer: (A)

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

  5. Question 5

    A biologist models the length of a certain fish species using a normal distribution with mean μ=20\mu = 20 cm and standard deviation σ=2\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?

    z=−1.5z = -1.5, indicating the value is 1.5 standard deviations below the mean

    z=−1.5z = -1.5, indicating the value is 1.5 standard deviations above the mean

    z=1.5z = 1.5, indicating the value is 1.5 standard deviations below the mean

    z=1.5z = 1.5, indicating the value is 1.5 standard deviations above the mean

    Show answer

    Answer: (A)

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

  6. 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?

    The value 550 is exactly two standard deviations above the mean

    The value 550 is exactly one standard deviation above the mean

    The sample size is large enough to apply the Central Limit Theorem

    The distribution is perfectly symmetric around the median of 500

    Show answer

    Answer: (A)

    The Empirical Rule states that 95% of data falls within 2 standard deviations. Since 550 is 2σ2\sigma above the mean (500+2(25)500 + 2(25)), the remaining 5% is split between the tails, leaving 2.5% in the upper tail.

  7. 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?

    P(−1.0<Z<2.0)P(-1.0 < Z < 2.0) using standard normal values

    P(−0.2<Z<0.4)P(-0.2 < Z < 0.4) using raw deviation values

    P(15.8<Z<16.4)P(15.8 < Z < 16.4) using raw variable values

    P(0.2<Z<0.4)P(0.2 < Z < 0.4) using standard error values

    Show answer

    Answer: (A)

    Standardizing the values gives z1=(15.8−16)/0.2=−1.0z_1 = (15.8-16)/0.2 = -1.0 and z2=(16.4−16)/0.2=2.0z_2 = (16.4-16)/0.2 = 2.0. The probability corresponds to the area between these two z-scores.

  8. Question 8

    A manufacturing process produces bolts with lengths that are normally distributed with a mean of 1010 mm and a standard deviation of 0.20.2 mm. Bolts are considered defective if they are shorter than 9.69.6 mm or longer than 10.410.4 mm. Based on the empirical rule, which claim about the production quality is best supported?

    Approximately 5%5\% of the bolts produced will be considered defective

    Approximately 2.5%2.5\% of the bolts produced will be considered defective

    Approximately 32%32\% of the bolts produced will be considered defective

    Approximately 0.3%0.3\% of the bolts produced will be considered defective

    Show answer

    Answer: (A)

    Applying the empirical rule to the boundaries 9.69.6 (μ−2σ\mu - 2\sigma) and 10.410.4 (μ+2σ\mu + 2\sigma) shows that 95%95\% of bolts fall within the acceptable range, leaving 5%5\% as defective.

  9. Question 9

    A student took two standardized tests. On Test A, the mean was 500500 with a standard deviation of 100100, and the student scored 650650. On Test B, the mean was 2020 with a standard deviation of 55, and the student scored 3232. Assuming both distributions are normal, which conclusion about the student's performance is most appropriate?

    Performance was stronger on Test B, indicated by a z-score of 2.42.4 versus 1.51.5

    Performance was stronger on Test A, indicated by a raw score of 650650 versus 3232

    Performance was stronger on Test A, indicated by a z-score of 1.51.5 versus 2.42.4

    Performance was equal on both tests, indicated by proportional scaling of scores

    Show answer

    Answer: (A)

    Calculating the z-scores reveals the student is 1.51.5 standard deviations above the mean on Test A and 2.42.4 above on Test B, indicating a relatively higher performance on Test B.

  10. Question 10

    Annual rainfall in a region is normally distributed with a mean of 4040 inches and a standard deviation of 44 inches. A drought is defined as a year with less than 3232 inches of rain. Based on the empirical rule, which claim about the frequency of droughts is supported?

    Drought conditions are expected to occur in approximately 2.5%2.5\% of years

    Drought conditions are expected to occur in approximately 5.0%5.0\% of years

    Drought conditions are expected to occur in approximately 16%16\% of years

    Drought conditions are expected to occur in approximately 0.15%0.15\% of years

    Show answer

    Answer: (A)

    Identifying that 3232 inches is 22 standard deviations below the mean (z=−2z = -2) leads to the conclusion that the area in the left tail is approximately 2.5%2.5\%.

What's on the AP Statistics Unit 2 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

  • 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)

Questions are drawn from 4197 multiple-choice questions and 25 FRQs written for Unit 2, Probability, Random Variables, and Probability Distributions.

Practice AP Statistics Unit 2 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

Review Unit 2 before you start

Other AP Statistics unit tests