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Yes, as you keep drawing more and more samples and the number of samples become sufficiently large. This is known as the Central Limit Theorem.

Q: Will sample means be nearly normally distributed if the distribution of the measurement among the individuals are not from a normal distribution?

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Yes, it is.

Also 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.

Errors are normally distributed with mean 0 .

It means that the probability distribution function of the variable is the Gaussian or normal distribution.

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Yes, it is.

Also normally distributed.

They are said to be Normally distributed.

No, but the approximation is better for normally distributed variables.

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.

Errors are normally distributed with mean 0 .

It means that the probability distribution function of the variable is the Gaussian or normal distribution.

A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.

It means that the data are distributed according to a probability distribution function known as the normal distribution. This site is useless for showing most mathematical functions but you can Google "normal distribution" to get more details.

The form of this question incorportates a false premise. The premise is that the data are normally distributed. Actually, is the sample mean which, under certain circumstances, is normally distributed.

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, because the two extremes of the phenotype distribution are selected against. Consider human height as an example of this type of selection and think of a normally distributed Bell curve.