Is it true or false that as the tails of the normal distribution curve are infinitely long, the total area under the curve is also infinite.
A normal distribution curve is a graphical representation of the probability of a continuous variable which has a probability defined by a Gaussian function with the highest concentration near values that lie at the mean.
The total probability of any variable is equal to 1 and can never exceed 1.
In a normal distribution curve, the tails of the curve are infinitely long but the area under them decreases at a very fast rate as the value of the variable deviates from the mean. The total area under the entire curve tends to 1 as the area under curve including the infinitely long tails is added up.
Because the tails of the normal distribution curve are infinitely long, the total area under the curve is also infinite.
The statement is false.
Do not confuse normal with normalized.
A normalized distribution curve has an area under the curve of exact number, 1, by definition.
This is becuase the probability of all the possible events is also always exactly 1.
In this case, the shape of the curve does not matter.
In probability theory, the normal (or Gaussian ) distribution is a continuous probability distribution that has a bell-shaped probability density function, known as the Gaussian function or informally the bell curve.