Features of Normal Distribution

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...