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CHAPTER 5 – SAMPLING DISTRIBUTIONS FOR MEANS
In section 1.3, we used normal probability tables to find probabilities for random variables from normally
distributed populations.
Population Distribution
The
population distribution
of a variable is the distribution of its values for all members of the
population. The population distribution is also the probability distribution of the variable when we choose
one individual from the population at random.
The Distribution of a Statistic
A statistic from a random sample or randomized experiment is a random variable.
The probability
distribution of the statistic is its sampling distribution.
If our random variable follows a normal distribution as in chapter 1.3, we can use the normal tables to
calculate probabilities.
In reality, however, our random variable seldom follows a normal distribution.
However, due to the central limit theorem, we are able to use the normal distribution in calculating
probabilities for statistics that come from nonnormal populations.
Central Limit Theorem
Draw an SRS of size
n
from any population with mean
µ
and finite standard deviation
σ
.
When
n
is large,
the sampling distribution of the sample mean
x
is approximately normal:
x
is approximately
(
,
)
N
n
σ
μ
In other words, when your sample size (
n
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 Spring '08
 Staff
 Normal Distribution, Probability, Standard Deviation, Variance, Probability theory

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