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Central limit theorem wikipedia, lookup

Daniel Jones, David Petersen, Derek
Peterson p.4
• A Normal curve is a density curve that is symmetric, unimodal,
and bell-shaped.
• Empirical Rule: 68% of data fall within one standard deviation
of the mean, 95% fall within 2 standard deviations, and 99.8%
fall within 3 standard deviations of the mean.
• The sampling distribution of p is the distribution that would
result from the average amount of successes in repeated
• For instance, our penny examples from class.
• Essentially the same as the sampling distribution of p, but
instead of recording the mean proportion of successes, we are
recording the mean number of successes.
• For both means and proportions, the greater the n, the smaller
the spread.
• When n is large, the sampling distribution of x-bar is
approximately Normal.
• Largeness of n depends on the size of the population.
• Generally, if n is greater than 30, the sample is large enough to
be approximately Normal.
• Family of curves whose spread is greater than that of the
Normal distribution.
• Symmetric, unimodal, centered at zero, and as n approaches
infinity, the t-distribution gets closer to being Normal.
• Use when performing tests or intervals with means when the
standard deviation is unknown.
• Family of distributions that take only positive values and are
skewed to the right. A specific chi-square distribution is
specified by one parameter, called degrees of freedom.
• Notes
• Textbooks