6.6: Chapter Review

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6.2: The Standard Normal Distribution

A \(z\)-score is a standardized value. Its distribution is the standard normal, \(Z \sim N(0,1)\). The mean of the \(z\)-scores is zero and the standard deviation is one. If \(z\) is the \(z\)-score for a value \(x\) from the normal distribution \(N(\mu, \sigma)\) then \(z\) tells you how many standard deviations \(x\) is above (greater than) or below (less than) \(\mu\).

6.4: Estimating the Binomial with the Normal Distribution

The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean \(\mu\) and the standard deviation \(\sigma\). A special normal distribution, called the standard normal distribution is the distribution of \(z\)-scores. Its mean is zero, and its standard deviation is one.

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6.2: The Standard Normal Distribution

6.4: Estimating the Binomial with the Normal Distribution