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Q: Why if a probability distribution curve is bell shaped why is this a normal distribution?

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bell shaped

Normal distribution is a perfectly symmetrical bell-shaped normal distribution. The bell curve is used to find the median, mean and mode of a function.

Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.

The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.

1. It is a probability distribution function and so the area under the curve must be 1.

Related questions

True * * * * * No. The Student's t-distribution, for example, is also bell shaped.

bell shaped

a Gaussian or 'normal' distribution

A normalized probability distribution curve has an area under the curve of 1.Note: I said "normalized", not "normal". Do not confuse the terms.

Normal distribution is a perfectly symmetrical bell-shaped normal distribution. The bell curve is used to find the median, mean and mode of a function.

Gaussian distribution. Some people refer to the normal distribution as a "bell shaped" curve, but this should be avoided, as there are other bell shaped symmetrical curves which are not normal distributions.

The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.

There are infinitely many sets of parameters that will generate a bell shaped curves - or near approximations. The Student's t or binomial, for large sample sizes get very close to the Gaussian distribution. There are others, too.

I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.

It is a symmetrical, "bell-shaped" curve. The tails are infinitely long.

Yes. The total area under any probability distribution curve is always the probability of all possible outcomes - which is 1.

No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.

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