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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


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 Statistics a bell shaped curve is said to be?

a Gaussian or 'normal' distribution


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.


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.


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.


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 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.


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.


What is the shape of a normal distribution?

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


What percentage of normally distributed scores lie under the normal curve?

100%. And that is true for any probability distribution.