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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.
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How the total area under the normal curve is equal to one?
Please see the link under "legitimate probability density function".
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 area under the standard normal curve?
the standard normal curve 2
What is the total area under the normal distribution curve?
The area under the normal distribution curve represents the probability of an event occurring that is normally distributed. So, the area under the entire normal distribution curve must be 1 (equal to 100%). For example, if the mean (average) male height is 5'10" then there is a 50% chance that a randomly selected male will have a height that is below or exactly 5'10". This is because the area under the normal curve from the left hand side up to the mean consists of half of the entire area of the normal curve. This leads us to the definitions of z-scores and standard deviations to represent how far along the normal curve a particular value is. We can calculate the likelihood of the value by finding the area under the normal curve to that point, usually by using a z-score cdf (cumulative density function) utility of a calculator or statistics software.
Is the total shape of a bell curve greater than 1?
It is assumed that by "shape" you mean "area". The quick answer is yes, probably. The "Bell curve" is called a Gaussian function (see related link). The area under a Gaussian is not necessarily 1; it can be anything. However, if you're talking about probability, where the probability distribution is in the same of a Gaussian, then the area under the curve must be exactly 1. This isn't however, because it is a bell curve, but because it's a probability distribution. The area under any probability distribution must always be exactly 1, or it isn't a valid distribution. The proper term for the total area under any curve f(x) is the integral from negative infinity to infinity of f(x) dx
