The Normal Distribution Is A Continuous, Unimodal And Symmetric Distribution

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The normal distribution is a continuous, unimodal and symmetric distribution. For a typical normal distribution, a mesokurtic (which means to have a moderate peak and tails for a graph), definition is one that has a mean of 0 and a standard deviation of 1. While this is the case, there might be other normal distributions with means that are not 0 and a standard deviation that is not 1, for these cases, we use their means and standard deviation. For example, if a normal distribution had a mean of -2 and a standard deviation of 3, then in order to clarify that it is indeed a normal distribution, we write N(-2,3). Among the normal distributions, we have a standard normal, exponential, uniform and beta. These are varieties of distributions we can get within a normal distribution based on factors like number of cases for example and where the cases were drawn from. At times when it gets complicated to distinguish between the standard deviation of a variable and that of a sampling distribution, there is a solution. The standard deviation for a sampling distribution is called a standard error and this literally means that if a sampling distribution is normal, then 68% of its samples will lie within one standard error of the mean and 98% within 1.98 standard error of the mean. The normal distribution is useful not just due a random variable following a normal distribution, but also because the Central Limit Theorem, which is a theorem that shows the sampling distribution of the mean
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