AP Statistics Flashcards: The Normal Distribution, Revisited
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 16 cards to help you master important concepts.
In a normal distribution, what does the area under the curve over a specific interval represent?
The area under a normal curve over an interval represents the probability that a value from the distribution lies in that interval.
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In a normal distribution, what does the area under the curve over a specific interval represent?
The area under a normal curve over an interval represents the probability that a value from the distribution lies in that interval.
When is it appropriate to use a normal distribution to approximate probabilities for an unknown distribution?
It is appropriate when the unknown distribution has characteristics similar to a normal distribution, such as being symmetrical and bell-shaped.
If you are given a specific area in a normal distribution, what are you being asked to determine?
You are being asked to determine the interval of values (the boundaries) that is associated with that given area under the curve.
What is the role of technology in working with normal distributions?
Technology (like a graphing calculator or software) can be used to quickly find the area for a given interval or determine the interval boundaries for a given area.
How do you calculate the probability that a particular value lies in a given interval of a normal distribution?
You calculate the area under the normal curve over that specific interval, often using z-scores or technology.
What is a continuous random variable?
A continuous random variable is a variable that can take any value within a specified domain.
What are two common methods for finding the interval boundaries for a given area in a normal distribution?
Interval boundaries for a given area can be found by using z-scores and a standard normal table, or by using statistical technology.
Why is the total area under any normal distribution curve equal to 1?
The total area represents the total probability of all possible outcomes, which must sum to 1 (or 100%).
What does it mean to find an interval for a 'given area'?
It means to find the specific range of values on the x-axis that corresponds to a given probability or proportion under the normal curve.
You need to find the probability that a machine part's length is outside a certain range. How would you approach this with a normal distribution?
You would calculate the area within the given interval and subtract it from 1, or calculate the areas in the two tails of the distribution directly.
How can intervals associated with a given area in a normal distribution be formally expressed?
These intervals can be determined and stated using appropriate inequalities to define the boundaries.
A problem asks for the range of values that represent the bottom 5% of a normally distributed dataset. What is the core task?
The core task is to determine the interval boundary (a z-score or value) associated with the lower 5% of the area in a normal distribution.
What is a 'bell-shaped curve'?
A bell-shaped curve is a graph that depicts a symmetrical probability distribution, where the mean, median, and mode are all located at the central peak.
To determine if a normal distribution is appropriate for a dataset, what visual characteristic would you look for in a histogram of the data?
You would look for a shape that is roughly symmetrical and bell-shaped, which suggests that using a normal distribution is appropriate.
What is the key characteristic of a normal approximation?
A normal approximation uses the properties of the normal distribution to estimate probabilities for other distributions that are similarly symmetrical and bell-shaped.
What shape describes a continuous random variable with a normal distribution?
A continuous random variable with a normal distribution is described by a symmetrical, bell-shaped curve.