Features of Normal Distribution
Normal distribution provides researchers with a single pattern of distribution. This makes it a popular model to use as a reference for observing a most frequent occurrence.
Step 1. Research
Use research from three to five scholarly sources cited in APA format to answer these questions about normal distributions:
What percentage of observations will fall within one, two, and three standard deviations of the mean in a normal distribution?
What is a z score?
How is the height of a normal distribution curve determined?
What is the relationship between probability and multiples of standard deviations of the mean in a normal distribution?
What are the “tails” of the normal distribution and why do outliers typically fall within them?
Step 2. Select
Select a digital tool to create your presentation of slides or other visuals.
Step 3. Design
Design your presentation visuals with the following :
Title
Explanation of the normal distribution
Illustration of the normal distribution with quartiles illustrating standard deviations about the mean
4-6 slides with explanations and/or illustrations addressing your research in Step 1
Summary
References
Include APA-formatted in-text citations on the slides where appropriate.
I will not be using powerpoint. Please use visuals.
Features of Normal Distribution
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Features of Normal Distribution
What percentage of observations will fall within one, two, and three standard deviations of the mean in a normal distribution?
A normal distribution has symmetrically distributed data with no skewness, with most values clustering around the central region. Data in a normal distribution obey the empirical rule, which states that approximately 68% of the observations lie within one standard deviation of the mean (µ ± σ), 95% lie under two standard deviations of the mean (µ ± 2σ) and 99.7% of the data observed lie under three standard deviations (µ ± 3σ) of the mean (Gravetter & Wallnau, 2017). This empirical rule is also known as the 68-95-99.7 rule.
Figure SEQ Figure \* ARABIC 1
The Empirical Rule
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What is a z score?
Z score, also known as the standard score, describes the position of a given observation from the mean of a normal distribution when measured in standard deviation units. It compares the scores on different variables by standardizing the distribution and is calculated using the formula z = (x-μ)/σ, where z is the z score, x is the value under evaluation, μ is the population mean, and σ is the standard deviation. If the value of the z score calculated is 0, it is on the mean (Mcleod, 2023). A positive z score shows that the observation's position is higher than the average mean, while a negative z score indicates that the raw score is below the average mean. Therefore, a standard normal distribution exhibits a normally shaped distribution with a mean of 0 and a standard deviation (SD) of 1.
How is the height of a normal distribution determined?
The probabili...