Normal Distribution
Definition
A normal distribution is a symmetric bell-shaped probability distribution characterized by its mean and standard deviation. It follows a specific mathematical formula called Gaussian distribution.
Analogy
Imagine you are measuring the heights of all the students in your school. If you were to plot a graph with height on the x-axis and the number of students on the y-axis, it would form a bell-shaped curve. This is similar to a normal distribution because most students' heights will be around the average, with fewer students being significantly taller or shorter.
Related terms
Standard Deviation: A measure of how spread out or dispersed data points are from the mean in a distribution.
Z-Score: A standardized value that represents how many standard deviations an individual data point is away from the mean in a normal distribution.
Central Limit Theorem: States that when independent random variables are added together, their sum tends to follow a normal distribution, regardless of the shape of their original distributions.
"Normal Distribution" appears in:
Subjects (1)
Study guides (14)
AP Statistics - 1.10 The Normal Distribution
AP Statistics - 4.7 Introduction to Random Variables and Probability Distributions
AP Statistics - 5.2 The Normal Distribution, Revisited
AP Statistics - 5.3 The Central Limit Theorem
AP Statistics - 5.5 Sampling Distributions for Sample Proportions
AP Statistics - 5.6 Sampling Distributions for Differences in Sample Proportions
AP Statistics - 5.7 Sampling Distributions for Sample Means
AP Statistics - 5.8 Sampling Distributions for Differences in Sample Means
AP Statistics - 6.1 Introducing Statistics: Why Be Normal?
AP Statistics - 7.2 Constructing a Confidence Interval for a Population Mean
AP Statistics - 7.3 Justifying a Claim About a Population Mean Based on a Confidence Interval
AP Statistics - 7.8 Setting Up a Test for the Difference of Two Population Means
AP Statistics - 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures
AP Statistics - 9.4 Setting Up a Test for the Slope of a Regression Model
Additional resources (4)
Practice Questions (9)
- In which scenario can you use the sampling distribution of the sample mean to model using a normal distribution?
- If the two population distributions can be modeled with a normal distribution, what can be inferred about the sampling distribution of the difference in sample means?
- Which measure is the center of a normal distribution?
- What does the standard deviation measure in a normal distribution?
- What does a z-score of -3 represent in a normal distribution?
- What does a z-score of 0 represent in a normal distribution?
- In a normal distribution, how can you determine intervals associated with a given area?
- The heights of adult males in a population follow a normal distribution with a mean of 175 cm and a standard deviation of 8 cm. What is the z-score for a male who is 185 cm tall?
- A normal distribution has a mean of 100 and a standard deviation of 20. What is the z-score for a data point that is at the 80th percentile?
Resources
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