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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 many standard deviations is the first quartile away from the mean on a Normal distribution?
0.674 sd.
Why is the Gaussian distribution referred to as normal distribution?
Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.
How many standard deviations is needed to capture 75 percent of data?
It depends on the shape of the distribution. For standard normal distribution, a two tailed range would be from -1.15 sd to + 1.15 sd.
How many standard normal distributions are there?
Only one. A normal, or Gaussian distribution is completely defined by its mean and variance. The standard normal has mean = 0 and variance = 1. There is no other parameter, so no other source of variability.
