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In which cases normal distribution is continuos and is not continuous?
The normal distribution is always continuous.
Does this means that all symmetric distribution are normal Explain?
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.
How the symmetric distribution is always normal?
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 total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
Is continuous distribution convert in discrete distribution?
If the question is asking if a continuous distribution can be converted to a discrete distribution, the answer is yes. Your age has a continuous distribution but in most cases, the information is recorded and analysed as if it were the whole number of years - a discrete distribution.
