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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.
An area of a normal probability distribution represents?
The number 1. The area of any probability distribution equals 1.
The total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
How is probability related to the area under the normal curve?
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.
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
