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Chapter 7 Central limit theorem The central limit theorem says that x can have any distribution whatsoever, but as the sample size gets larger and larger, the distribution of x bar will approach a normal distribution. (For more information, review Section 7.5) Continuity correction Adjusting the values of discrete random variables to obtain a corresponding range for a continuous random variable is called making a continuity correction. If the discrete variable is a left point of an interval, subtract 0.5 to obtain the corresponding normal variable. If the discrete variable is a right point of an interval, add 0.5 to obtain the corresponding normal variable. (For more information, review Section 7.6) Empirical rule For a distribution that is symmetrical and bell-shaped (in particular, for a normal distribution): Approximately 68% of the data values will lie within one standard deviation on each side of the mean. Approximately 95% of the data values will lie within two standard deviations on each side of the mean. Approximately 99.7% (or almost all) of the data values will lie within three standard deviations on each side of the mean. (For more information, review Section 7.1) z value or z score The z value or z score gives the number of standard deviations between the original measurement x and the mean of the x distribution. (For more information, review Section 7.2) Left-tail style table A left-tail style table gives cumulative areas to the left of a specified z. (For more information, review Section 7.2) Normal curve The graph of a normal distribution is called a normal curve. (For more information, review Section 7.1) Normal distribution One of the most important examples of a continuous probability distribution is the normal distribution. (For more information, review Section 7.1) Normal quantile plot A normal quantile plot is an indicator that can be used to determine if data have a normal distribution. For data that approximately havea a normal distribution, the normal quantile plot of the data should have points close to a straight line. (For more information, review Section 7.3) Pearson's index Pearson's index is a measure of skewness for sample data. Normal distributions are symmetric and should have a Pearson's index value between –1 and 1. (For more information, review Section 7.3) Raw score The raw score is the value of a random variable in a non-standard normal distribution. The raw score can be converted into a z score. (For more information, review Section 7.2) Sampling distribution A sampling distribution is a probability distribution of a sample statistic based on all possible simple random samples of the same size from the same population. (For more information, review Section 7.4) Standard error The standard error is another name for the standard deviation of the x bar distribution. (For more information, review Section 7.5) Standard normal distribution The standard normal distribution is a normal distribution with mean 0 and standard deviation 1. (For more information, review Section 7.2) Unbiased A sample statistic is unbiased if the mean of its sampling distribution equals the value of the parameter being estimated. (For more information, review Section 7.5)