1. mu (population mean) 2. sigma (population standard deviation)
You cannot. It has a characteristic bell-shaped curve but so does a Student's t with enough degrees of freedom. There are other distributions which, with suitable choice of parameters can be made to look very similar to the Normal curve.
Mean and Standard Deviation
a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
In science, "normal" typically means something that is within expected parameters or conforms to a standard. For example, a "normal distribution" refers to a bell-shaped curve that represents the expected distribution of a set of data points.
It is a symmetric function which is fully described by two parameters. It is called bell shape but I have never seen a bell whose rime is infinitely far away from its apex. The area under the curve is equal to 1.
The standard normal curve is symmetrical.
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
According to the Central Limit Theorem, if you take measurements for some variable from repeated samples from any population, the mean values have a probability distribution which is known as the Gaussian distribution. Because of the fact that it is found often it is also called the Normal distribution. It is a symmetric distribution which is fully determined by two parameters: the mean and variance (or standard deviation). It is also sometimes referred to as the bell curve although I have yet to see a bell that stretches out at its bottom towards infinity!The normal distribution can be used for the heights or masses of people, for examination scores.
It is a normal curve with mean = 0 and variance = 1.
There is no minimum number: very few observations can be indicative. As the population number increases the observations should get closer to the Normal distribution. You should have 30 or so observations to get a smooth-ish curve.
the standard normal curve 2