# Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

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Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  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 = , the same as the mean of X Variance =  2 /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.

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