AP Statistics Practice Quiz: The Normal Distribution, Revisited
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) The probability that a random variable falls within that interval of values.
B) The mean of the distribution.
C) The standard deviation of the distribution.
D) The total number of possible outcomes.
Correct Answer: A
Based on the provided content, 'The area under a normal curve over an interval represents the probability that a value lies in that interval.'
A) A variable that can only take a finite number of specific values.
B) A variable that can take any value within a given range or domain.
C) A variable that is always represented by a bell-shaped curve.
D) A variable that represents counts of events, such as the number of heads in 10 coin flips.
Correct Answer: B
The provided content states, 'A continuous random variable can take any value within a specified domain.' Options A and D describe discrete random variables. Option C is only true for normally distributed continuous variables.
A) When the other distribution is for a discrete random variable.
B) When the mean of the other distribution is zero.
C) When the other distribution has characteristics that are symmetrical and bell-shaped.
D) When the standard deviation of the other distribution is exactly 1.
Correct Answer: C
The content explicitly states that 'Normal distributions can be used to approximate other distributions with similar symmetrical, bell-shaped characteristics.'
A) The mean and the mode only.
B) The range of the dataset.
C) Z-scores or statistical technology.
D) The shape of the distribution alone.
Correct Answer: C
The content mentions that 'Interval boundaries for a given area in a normal distribution can be found using z-scores or technology.' The middle 95% is a given area, so this method applies directly.
A) To determine the standard deviation of the distribution.
B) To find the mean of the random variable X.
C) To calculate the probability that a particular value of X lies in the interval [a, b].
D) To verify that the distribution is symmetrical.
Correct Answer: C
This question directly tests two content points: 'Calculate the probability that a particular value lies in a given interval of a normal distribution' and 'The area under a normal curve over an interval represents the probability that a value lies in that interval.'
A) P(X < k) = 0.05
B) P(X > k) = 0.05
C) P(-k < X < k) = 0.95
D) P(X = k) = 0.05
Correct Answer: B
The 'top 5%' corresponds to the area in the right tail of the distribution. This is represented by the probability that the variable X is greater than some value k. The content states that 'Intervals associated with a given area in a normal distribution can be determined using appropriate inequalities.'
A) Because the variable (number of errors) is continuous.
B) Because the normal distribution cannot be used in quality control.
C) Because the data's distribution is not symmetrical and bell-shaped.
D) Because the mean and median of the data are likely equal.
Correct Answer: C
The content specifies that a normal distribution is appropriate for approximating distributions with 'symmetrical, bell-shaped characteristics.' A highly skewed distribution lacks the necessary symmetry, making the normal approximation inappropriate.
A) A uniform, rectangular shape.
B) A symmetrical, bell-shaped curve.
C) A right-skewed curve.
D) A bimodal, two-peaked curve.
Correct Answer: B
The content states, 'A continuous random variable with a normal distribution is described by a bell-shaped curve.'
A) The exact number of questions the student answered correctly.
B) The interval of scores below the student's score, which corresponds to 90% of the area under the curve.
C) The total number of students who took the test.
D) That the distribution of scores is skewed to the left.
Correct Answer: B
This is an application of the principle to 'Determine the interval associated with a given area in a normal distribution.' The 90th percentile means 90% of the area under the curve is to the left of the student's score, defining the interval of scores below that point.
A) Calculate the mean and standard deviation of the distribution.
B) Use a z-table or technology to find the z-score corresponding to a right-tail area of 0.25.
C) Assume 'x' is 0.25 because probability equals the value.
D) Find the area between -0.25 and 0.25.
Correct Answer: B
This question combines the idea of using inequalities with the method for finding boundaries. The problem is to find the boundary 'x' for a given area (0.25 in the right tail), which is done using z-scores (from a table) or technology.
A) It is equal to the mean of the distribution.
B) It represents a probability of 1, or 100% of all possible outcomes.
C) It is equal to the standard deviation of the distribution.
D) It is an infinitely large number.
Correct Answer: B
The content states that 'The area under a normal curve over an interval represents the probability that a value lies in that interval.' By extension, the area over the entire interval of all possible values must be equal to 1, representing the total probability.
A) If a small sample of bird weights shows a skewed distribution.
B) If the variable, bird weight, is a continuous variable.
C) If the population distribution is unknown but can be reasonably assumed to be symmetrical and bell-shaped.
D) If the mean weight is greater than the median weight.
Correct Answer: C
This question requires synthesizing two points. The content states one must 'Determine the appropriateness of using the normal distribution' and that it can be used to approximate distributions with 'symmetrical, bell-shaped characteristics.' Therefore, assuming these characteristics provides the justification.
A) Find the area under the normal curve over the interval from 20 to 30.
B) Calculate the z-score for the mean commute time.
C) Determine the 50th percentile of the data.
D) Identify the mode of the distribution.
Correct Answer: A
This is a direct application of the content point: 'Calculate the probability that a particular value lies in a given interval of a normal distribution.' The proportion is equivalent to the probability, which is found by calculating the area under the curve for that interval.
A) All continuous random variables follow a normal distribution.
B) A normal distribution describes a specific type of continuous random variable characterized by a bell-shaped curve.
C) A continuous random variable is bell-shaped, while a normal distribution can take any shape.
D) Normal distributions apply to discrete variables, while continuous variables are described by other curves.
Correct Answer: B
A continuous random variable can have many different distributions. A normal distribution is a specific, common model for a continuous random variable, identified by its bell shape. Therefore, a normal distribution is a specific instance of a model for a continuous random variable.
A) The probability that a product's lifespan is exactly one year.
B) The area under the normal curve for the interval of lifespans from zero to one year.
C) The z-score corresponding to the mean lifespan.
D) The interval associated with the middle 50% of product lifespans.
Correct Answer: B
This problem requires one to 'Calculate the probability that a particular value lies in a given interval.' The interval of interest is from the start (time 0) to one year. The area under the curve over this interval gives the probability of failure within the first year.
A) Calculating the mean of the distribution.
B) Determining the interval associated with a given area.
C) Approximating an unknown distribution.
D) Describing the shape of a bell curve.
Correct Answer: B
This is a direct description of the process outlined in the content: 'Determine the interval associated with a given area in a normal distribution.' The given area is 0.75 (or 75%), and the goal is to find the boundary value of the interval from negative infinity up to that point.