246 CHAPTER 6 Normal Probability Distributions 6-4 The Central Limit Theorem • Describe the central limit theorem. • Apply the central limit theorem by finding the probability that a sample mean falls within some specified range of values. • Identify conditions for which it is appropriate to use a normal distribution for the distribution of sample means. 6-5 Assessing Normality • Develop the ability to examine histograms, outliers, and normal quantile plots to determine whether sample data appear to be from a population having a distribution that is approximately normal. 6-6 Normal as Approximation to Binomial (available at www.TriolaStats.com) • Identify conditions for which it is appropriate to use a normal distribution as an approximation to a binomial probability distribution. • Use the normal distribution for approximating probabilities for a binomial distribution. Key Concept In this section we present the standard normal distribution, which is a specific normal distribution having the following three properties: 1. Bell-shaped: The graph of the standard normal distribution is bell-shaped (as in Figure 6-1). 2. m = 0: The standard normal distribution has a mean equal to 0. 3. s = 1: The standard normal distribution has a standard deviation equal to 1. In this section we develop the skill to find areas (or probabilities or relative frequencies) corresponding to various regions under the graph of the standard normal distribution. In addition, we find z scores that correspond to areas under the graph. These skills become important in the next section as we study nonstandard normal distributions and the real and important applications that they involve. Normal Distributions There are infinitely many different normal distributions, depending on the values used for the mean and standard deviation. We begin with a brief introduction to this general family of normal distributions. 6-1 The Standard Normal Distribution m Value Curve is bell-shaped and symmetric FIGURE 6-1 The Normal Distribution DEFINITION If a continuous random variable has a distribution with a graph that can be described by the equation given as Formula 6-1 (shown on the next page), we say that it has a normal distribution. A normal distribution is bell-shaped and symmetric, as shown in Figure 6-1.
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