Yes, to approximately standard normal.
If the random variable X is approximately normal with mean m and standard deviation s, then
(X - m)/s
is approximately standard normal.
There are many variables that are not normally distributed. You can describe them using a probability distribution function or its cumulative version; you can present them graphically.
Yes, it is.
When studying the sum (or average) of a large number of independent variables. A large number is necessary for the Central Limit Theorem to kick in - unless the variables themselves were normally distributed. Independence is critical. If they are not, normality may not be assumed.
The easiest way to tell if data is normally distributed is to plot the data.line plot apex
Normally distributed.
The sum of two random variables that are normally distributed will be also be normally distributed. Use the link and check out the article. It'll save a cut and paste.
No, but the approximation is better for normally distributed variables.
YES.
There are many variables that are not normally distributed. You can describe them using a probability distribution function or its cumulative version; you can present them graphically.
Yes, and the new distribution has a mean equal to the sum of the means of the two distribution and a variance equal to the sum of the variances of the two distributions. The proof of this is found in Probability and Statistics by DeGroot, Third Edition, page 275.
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.
Yes, it is.
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
The value of a roll of two dice is normally distributed.
When studying the sum (or average) of a large number of independent variables. A large number is necessary for the Central Limit Theorem to kick in - unless the variables themselves were normally distributed. Independence is critical. If they are not, normality may not be assumed.
...normally distributed.
NO!