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Jan 15, 2013 · It then defines terms and symbols used in the normal distribution, including mean, standard deviation, and z-scores. The document explains the characteristics of the normal distribution graphically and provides examples of finding areas under the normal curve using z-tables.
Jun 27, 2016 · The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean and standard deviation. Many real-world variables are approximately normally distributed.
Jul 15, 2023 · Normal distribution: - Certain data, when graphed as a histogram (data on the horizontal axis, frequency on the vertical axis), creates a bell-shaped curve known as a normal curve, or normal distribution. - Two parameters define the normal distribution, the mean (µ) and the standard deviation (σ).
For normal distributions we tend to draw the 𝑦 axis at the mean for symmetry. 5 What does it look like? 𝑓 (𝑥) Compare for example the blue and red curve.
- Example 1: Birthweight of Babies
- Example 2: Height of Males
- Example 3: Shoe Sizes
- Example 4: Act Scores
- Example 5: Average NFL Player Retirement Age
- Example 6: Blood Pressure
- Additional Resources
It’s well-documented that the birthweight of newborn babies is normally distributed with a mean of about 7.5 pounds. The histogram of the birthweight of newborn babies in the U.S. displays a bell-shape that is typically of the normal distribution:
The distribution of the height of males in the U.S. is roughly normally distributed with a mean of 70 inches and a standard deviation of 3 inches. A histogram of the height of all U.S. male reveals a bell shape:
The distribution of shoe sizes for males in the U.S. is roughly normally distributed with a mean of size 10 and a standard deviation of 1. A histogram of the shoe sizes of all U.S. male reveals a bell shape with a single peak at size 10:
The distribution of ACT scores for high school students in the U.S. is normally distributed with a mean of 21 and a standard deviation of about 5. A histogram of the ACT scores for all U.S. high school students illustrates this normal distribution:
The distribution of retirement age for NFL players is normally distributed with a mean of 33 years old and a standard deviation of about 2 years. A histogram of this distribution exhibits a classical bell shape:
The distribution of diastolic blood pressure for men is normally distributed with a mean of about 80 and a standard deviation of 20. A histogram of the distribution of blood pressures for all mean displays a normal distribution with a bell shape:
The following tutorials share examples of other probability distributions in real life: 5 Real-Life Examples of the Poisson Distribution 5 Real-Life Examples of the Binomial Distribution 5 Real-Life Examples of the Geometric Distribution 5 Real-Life Examples of the Uniform Distribution
Oct 23, 2020 · In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center. Normal distributions are also called Gaussian distributions or bell curves because of their shape.
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Oct 11, 2023 · A bell-shaped curve, also known as a normal distribution or Gaussian distribution, is a symmetrical probability distribution in statistics. It represents a graph where the data clusters around the mean, with the highest frequency in the center, and decreases gradually towards the tails.
