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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 sampling. • 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