What Normal curve is
The normal curve is a type of probability distribution that is symmetrical, bell-shaped, and centered at its mean. It is also known as the Gaussian or the bell curve.
The normal curve is used to model the probability distribution of many real-world phenomena, such as height and IQ scores. It is important to note that the normal curve is idealized, and that real-world data often deviates from it.
Steps to draw a normal curve:
- Calculate the mean, median, and standard deviation of your data set.
- Plot the mean of your data set on the x-axis.
- Draw a bell-shaped curve centered on the mean.
- Shade the area between one (1) standard deviation above and one (1) standard deviation below the mean.
- Shade the area between two (2) standard deviations above and two (2) standard deviations below the mean.
- Shade the area between three (3) standard deviations above and three (3) standard deviations below the mean.
- Label the x-axis and y-axis with the appropriate values.
Examples
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A Normal curve is used to model the probability of a given event occurring in a continuous random variable. For example, in a standard normal distribution, 68% of all data points fall within one standard deviation of the mean, 95% of all data points fall within two standard deviations of the mean, and 99.7% of all data points fall within three standard deviations of the mean.
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A Normal curve is used to determine the probability of a certain score falling within a given range in a standardized test. For example, the probability of a student scoring between 70 and 80 on a test with a mean of 75 and a standard deviation of 10 would be determined by the Normal curve.
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A Normal curve is used to describe the probability of a random variable falling within a certain range. For example, a Normal curve can be used to describe the probability of a person’s height falling within a given range.