Download Normal and Sampling Distributions

Normal and Sampling
Distributions
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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
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A sampling distribution is the probability
distribution of a random variable that is
a sample statistic
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Sample
Sample
Sample
Sample
mean
proportion
standard deviation
correlation coefficient
Central Limit Theorem
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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
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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
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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.