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A normal distribution is sometimes informally called a bell curve. [8] However, many other distributions are bell-shaped (such as the Cauchy , Student's t , and logistic distributions). (For other names, see Naming .)
In educational statistics, a normal curve equivalent (NCE), developed for the United States Department of Education by the RMC Research Corporation, [1] is a way of normalizing scores received on a test into a 0-100 scale similar to a percentile rank, but preserving the valuable equal-interval properties of a z-score. It is defined as:
This is the meaning of "normal" in the phrases rational normal curve and rational normal scroll. Every regular scheme is normal. Conversely, Zariski (1939, theorem 11) showed that every normal variety is regular outside a subset of codimension at least 2, and a similar result is true for schemes. [1] So, for example, every normal curve is regular.
Normal distributions are symmetrical, bell-shaped distributions that are useful in describing real-world data. The standard normal distribution, represented by Z, is the normal distribution having a mean of 0 and a standard deviation of 1.
The term "curve" refers to the bell curve, the graphical representation of the probability density of the normal distribution, but this method can be used to achieve any desired distribution of the grades – for example, a uniform distribution.
A graphical tool for assessing normality is the normal probability plot, a quantile-quantile plot (QQ plot) of the standardized data against the standard normal distribution. Here the correlation between the sample data and normal quantiles (a measure of the goodness of fit) measures how well the data are modeled by a normal distribution. For ...
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.
If the tail behavior is the main interest, the student t family can be used, which approximates the normal distribution as the degrees of freedom grows to infinity. The t distribution, unlike this generalized normal distribution, obtains heavier than normal tails without acquiring a cusp at the origin. It finds uses in plasma physics under the ...