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Questions and Answers
What is the value of the median and mode in a normal distribution?
What is the value of the median and mode in a normal distribution?
What percentage of data falls within 2 standard deviations of the mean in a normal distribution?
What percentage of data falls within 2 standard deviations of the mean in a normal distribution?
What is the purpose of a Z-score in a normal distribution?
What is the purpose of a Z-score in a normal distribution?
What is a characteristic of the normal distribution?
What is a characteristic of the normal distribution?
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What is the relationship between the normal distribution and the binomial distribution?
What is the relationship between the normal distribution and the binomial distribution?
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In which field is the normal distribution commonly used?
In which field is the normal distribution commonly used?
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What is the purpose of the null hypothesis in a statistical test?
What is the purpose of the null hypothesis in a statistical test?
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What is the alternative hypothesis in a two-tailed test?
What is the alternative hypothesis in a two-tailed test?
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What is the consequence of a Type I error?
What is the consequence of a Type I error?
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What is the probability of a Type I error represented by?
What is the probability of a Type I error represented by?
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What does a p-value represent?
What does a p-value represent?
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What is the consequence of a Type II error?
What is the consequence of a Type II error?
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Study Notes
Normal Distribution
Definition
- A continuous probability distribution that is symmetric and bell-shaped
- Also known as the Gaussian distribution or bell curve
- Describes how variables are distributed in a population
Key Features
- Mean (μ): the average value of the distribution
- Standard Deviation (σ): a measure of the spread or dispersion of the data
- Median and mode are equal to the mean
- 68-95-99.7 Rule: approximately 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean
Properties
- The normal distribution is symmetric around the mean
- The curve is continuous and smooth
- The distribution is asymptotic, meaning it approaches but never touches the x-axis
- The normal distribution is a limiting case of the binomial distribution
Z-Scores
- A measure of how many standard deviations an observation is away from the mean
- Calculated using the formula: z = (x - μ) / σ
- Used to compare observations from different normal distributions
- Z-scores can be used to find the percentile or probability of an observation
Applications
- Modeling real-valued variables in natural and social sciences
- Analyzing data that is normally distributed or can be transformed to normality
- Used in statistical inference, hypothesis testing, and confidence intervals
- Applications in finance, engineering, medicine, and social sciences
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Description
Test your understanding of the normal distribution, its properties, and applications in various fields. Learn about mean, standard deviation, z-scores, and more.
