Yes, it is.
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
Your question may be a little overly complex. Usually you start with some degree of confidence that the variable(s) you are studying are normally distributed; you don't do an experiment and wait for the results to tell you. Your confidence that a variable is normally distributed helps you to determine whether or not your results are significantly different from what you would expect by chance. If I have missed the meaning of your question, my apologies.
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.
Yes, it is.
x
The value of a roll of two dice is normally distributed.
no
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
No, it does not. In fact, for many statistical analyses, it is a definite advantage.
Your question may be a little overly complex. Usually you start with some degree of confidence that the variable(s) you are studying are normally distributed; you don't do an experiment and wait for the results to tell you. Your confidence that a variable is normally distributed helps you to determine whether or not your results are significantly different from what you would expect by chance. If I have missed the meaning of your question, my apologies.
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.
Given "n" random variables, normally distributed, and the squared values of these RV are summed, the resultant random variable is chi-squared distributed, with degrees of freedom, k = n-1. As k goes to infinity, the resulant RV becomes normally distributed. See link.
It is 0.37, approx.
Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.