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Chapter 6 Outline Identify distributions as symmetrical or skewed Identify the properties of the normal distribution Find the area under the standard normal distribution given various z values Find the probabilities for a normally distributed variable by transforming it into a standard normal variable Find specific data values for given percentages using the standard normal distribution Use the central limit theorem to solve problems involving sample means for large samples Use the normal approximation to compute probabilities for a binomial variable Introduction Many continuous variables have distributions that are bell-shaped and are called approximately normally distributed variables A normal distribution is also known as the bell curve or the Gaussian distribution Normal and Skewed Distributions The normal distribution is a continuous bell-shaped distribution of a variable If the data values are evenly distributed about the mean the distribution is said to be symmetrical If the majority of the data values fall to the left or right of the mean the distribution is said to be skewed Left Skewed Distributions When the majority of the data values fall to the right of the mean the distribution is said to be negatively or left skewed The mean is to the left of the median and the mean and the median are to the left of the mode Right Skewed Distributions When the majority of the data values fall to the left of the mean the distribution is said to be positively or right skewed The mean falls to the right of the median and both the mean and the median fall to the right of the mode Equation for a Normal Distribution The mathematical equation for the normal distribution is Properties of the Normal Distribution The shape and position of the normal distribution curve depend on two parameters the mean and the standard deviation Each normally distributed variable has its own normal distribution curve which depends on the values of the variables mean
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