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.
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
normal_distribution
There is no particular meaning associated with theta - it will depend on the context.
IQ is normally distributed in the general population. Age is not.
No, the normal distribution is strictly unimodal.
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
normal_distribution
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
The normal distribution is a statistical distribution. Many naturally occurring variables follow the normal distribution: examples are peoples' height, weights. The sum of independent, identically distributed variables - whatever their own underlying distribution - will tend towards the normal distribution as the number in the sum increases. This means that the mean of repeated measures of ANY variable will approach the normal distribution. Furthermore, some distributions that are not normal to start with, can be converted to normality through simple transformations of the variable. These characteristics make the normal distribution very important in statistics. See attached link for more.
A researcher wants to go from a normal distribution to a standard normal distribution because the latter allows him/her to make the correspondence between the area and the probability. Though events in the real world rarely follow a standard normal distribution, z-scores are convenient calculations of area that can be used with any/all normal distributions. Meaning: once a researcher has translated raw data into a standard normal distribution (z-score), he/she can then find its associated probability.
There is no particular meaning associated with theta - it will depend on the context.
The standard normal distribution is a normal distribution with mean 0 and variance 1.
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
IQ is normally distributed in the general population. Age is not.
le standard normal distribution is a normal distribution who has mean 0 and variance 1
When its probability distribution the standard normal distribution.
No, the normal distribution is strictly unimodal.