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No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

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No. There are many symmetrical distributions that are not Normal. A simple one is the uniform distribution:

Q: Are all symmetric distribution are normal?

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They are both continuous, symmetric distribution functions.

No. The Normal distribution is symmetric: skewness = 0.

The t-distribution is symmetric so the question is irrelevant.The t-distribution is symmetric so the question is irrelevant.The t-distribution is symmetric so the question is irrelevant.The t-distribution is symmetric so the question is irrelevant.

Yes. However, because the distribution is symmetric about 0, some tables give only positive values for z.

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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.

Symmetric

The Normal distribution is, by definition, symmetric. There is no other kind of Normal distribution, so the adjective is not used.

They are all the same.

No, not all distributions are symmetrical, and not all distributions have a single peak.

Mean

The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.

The data from a normal distribution are symmetric about its mean, not about zero. There is, therefore nothing strange about all the values being negative.

The Normal ditribution is symmetric but so are other distributions.

It is a continuous parametric distribution belonging to the family of exponential distributions. It is also symmetric.

They are both continuous, symmetric distribution functions.