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## Normal and Sampling Distributions

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**Normal and Sampling Distributions**• A normal distribution is uniquely determined by its mean, m, and variance, s2 • The random variable Z = (X-m)/s is normal with mean 0 and variance 1 • The normal probability density function is defined on page 227 and integrated in Table E.2 on page 834**Sampling Distributions**• A sampling distribution is the probability distribution of a random variable that is a sample statistic • Sample mean • Sample proportion • Sample standard deviation • Sample correlation coefficient**Central Limit Theorem**• The sampling distribution of the sample mean is approximately normal • The larger the sample size, n, the more closely the sampling distribution of the sample mean will resemble a normal distribution.**The Sampling Distribution of the Sample Mean**• Mean = m, the same as the mean of X • Variance = s2/n, the variance of X divided by sample size**The Sampling Distribution of the Sample Proportion**• Mean = p, the population proportion of or the probability of success in the binomial trial • Variance = p(1-p)/n. • The binomial distribution is approximately normal if np and n(1-p) are both at least 5.