## MATH 399N Week 5 Discussion Topic: Interpreting Normal Distributions → Spring 2017

MATH 399N Week 5 Discussion: Interpreting Normal Distributions

Professor and class,

The z-Score and the Central Limit Theorem.

The Central Limit Theorem is a very important theorem in statistics. It basically confirms what might be an intuitive truth to you: that as you increase the sample size for a random variable, the distribution of the sample means better approximates a normal distribution

As the sample size, n, increases, the resulting sampling distribution would approach a normal distribution with the same mean as the population and with σx¯=σn√. The notation σx¯ reminds you that this is the standard deviation of the distribution of sample means and not the standard deviation of a single observation

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