The central limit theorem: the arithmetic mean of a sufficient number of independent random variables with means and variances will be a normal random variable. It's just that lots of natural phenomena are like this, or appear to be sufficiently like this. Please see the wikipedia article for more details.
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The standard normal curve is symmetrical.
It is a normal curve with mean = 0 and variance = 1.
the standard normal curve 2
Answer this question...similarities and differences between normal curve and skewness
A bell shaped probability distribution curve is NOT necessarily a normal distribution.