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from class: Intro to Statistics Definition A normally distributed variable follows a symmetric, bell-shaped curve where most values cluster around the mean. It is characterized by its mean and standard deviation.
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Predict what's on your test 5 Must Know Facts For Your Next Test The total area under the normal distribution curve is equal to 1. Approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three. The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases. In hypothesis testing, if a population is normally distributed, z-scores can be used to determine probabilities. A normal distribution is denoted as $N(\mu, \sigma^2)$ where $\mu$ is the mean and $\sigma^2$ is the variance. Review Questions What percentage of data falls within two standard deviations of the mean in a normal distribution? How does the Central Limit Theorem relate to normally distributed variables? Why is it important to know if a dataset follows a normal distribution when conducting hypothesis tests? "Normally distributed" also found in:
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