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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.
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What does even distribution mean?
It means that the probability density function is symmetric about 0.
The distribution of sample means is not always a normal distribution Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal if the number of samples does not reach 30.
What is the distribution with an means of 0 and a standard deviation of 1?
It is called a standard normal distribution.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
Is the distribution of sample means always a normal distribution If not why?
It need not be if: the number of samples is small; the elements within each sample, and the samples themselves are not selected independently.
Does this means that all symmetric distribution are normal?
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What does even distribution mean?
It means that the probability density function is symmetric about 0.
The distribution of sample means is not always a normal distribution Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal if the number of samples does not reach 30.
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
Explain how you could create a distribution of means by taking a large number of samples of four individuals each?
As the sample size increases, and the number of samples taken increases, the distribution of the means will tend to a normal distribution. This is the Central Limit Theorem (CLT). Try out the applet and you will have a better understanding of the CLT.
What is the probability that a tree's height exceeds the mean?
If the distribution of heights were symmetric then it would be 1/2 but the distribution is not at all likely to be symmetric. There will by many young trees of varying heights whereas the mature trees are likely to reach similar heights. The distribution is, therefore, likely to be negatively skewed, which means that the probability is greater than 1/2.
Electric field inside the cylinder which is cylindrically symmetric?
For a cylindrically symmetric charge distribution, the electric field inside the cylinder is also cylindrically symmetric. This means that the electric field points radially outwards or inwards along the axis of the cylinder with the magnitude dependent on the charge distribution. The electric field can be calculated using Gauss's law and applying symmetry arguments to simplify the problem.
What is the distribution with an means of 0 and a standard deviation of 1?
It is called a standard normal distribution.
Is water a symmetric compound?
Yes, water is a symmetric compound with a bent molecular geometry. This means that the oxygen atom is at the center and the two hydrogen atoms are located on one side, resulting in an uneven distribution of charge within the molecule.
Compounds which have symmetric distribution in charge and are NOT soluble in water?
Nonpolar molecules, such as hydrocarbons like hexane or octane, typically have symmetric charge distributions due to the equal sharing of electrons in covalent bonds. These substances are generally not soluble in water because their nonpolar nature does not allow them to interact favorably with the polar water molecules.
Why is the normal probability distribution called a family of normal probability distribution?
Because very many variables tend to have the Gaussian distribution. Furthermore, even if the underlying distribution is non-Gaussian, the distribution of the means of repeated samples will be Gaussian. As a result, the Gaussian distributions are also referred to as Normal.
Can one treat sample means as a normal distribution?
Not necessarily. It needs to be a random sample from independent identically distributed variables. Although that requirement can be relaxed, the result will be that the sample means will diverge from the Normal distribution.
