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Is a normally distributed variable needed to have a normally distributed sampling distribution.?
Yes, it is.
Can you think of a variable that is normally distributed?
The value of a roll of two dice is normally distributed.
Is it true that the mean of a normally distributed variable can be any real number?
no
How to present a variable that is not normally distributed?
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.
What does it mean when you say a variable is normally distributed?
It means that the probability distribution function of the variable is the Gaussian or normal distribution.
Does it matter if your dependent variable is normally distributed?
No, it does not. In fact, for many statistical analyses, it is a definite advantage.
What do results tell you with regard to whether the data is normally distributed?
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.
Why is the central limit theorem an important idea for dealing with a population not normally distributed?
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.
When doing a t-test what does normal distributed in population 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.
How chi square distribution is extension of normal distribution?
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.
What is the probabilty that the individuals pressure will be between 120 and 121.8 if the mean pressure is 120 and the standard deviation is 5.6 with a normally distributed variable?
It is 0.37, approx.
What you mean by saying random variable is approximately normally distributed?
Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.
