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A bell shaped probability distribution curve is NOT necessarily a normal distribution.

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

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


What is the shape of normal probability curve?

bell shaped


In Statistics a bell shaped curve is said to be?

a Gaussian or 'normal' distribution


What does area have to do with probability?

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


In a perfectly symmetrical bell-shaped normal distribution?

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.


Another name for the Normal Distribution?

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.


What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

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.


Why is A bell shaped probability distribution curve is NOT necessarily a normal distribution?

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.


Define a normal random variable?

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.


What is the shape of a normal distribution?

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


Is in the normal distribution the total area beneath the curve represent the probability for all possible outcomes for a given event?

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


Normal curve is the meaning of standard normal distribution?

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

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