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If random samples of size n = 36 are drawn from a nonnormal population with finite mean 
and standard deviation 
, then the sampling distribution of the sample mean 
is approximately normally distributed with mean 
and standard deviation 
Sampling Distribution
The probability distribution of a given statistic based on a random sample, used to make inferences about a population.
Nonnormal Population
A population distribution that does not fit the normal (bell-shaped) distribution pattern, often having skewness or kurtosis.
Approximately Normally Distributed
Describing data that roughly follows a bell curve, with most values clustering around a central mean.
- Perceive the significance and role of the Central Limit Theorem (CLT) in statistical inference, mainly its effects on the contour of the sampling distribution.
- Comprehend the impact of sample size on the sampling distribution, including effects on the standard error and the shape of the distribution.
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Learning Objectives
- Perceive the significance and role of the Central Limit Theorem (CLT) in statistical inference, mainly its effects on the contour of the sampling distribution.
- Comprehend the impact of sample size on the sampling distribution, including effects on the standard error and the shape of the distribution.
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