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By the Central Limit Theorem if is sufficiently large, has approximately a normal distribution with and
The larger the value of the better the approximation.
The Central Limit Theorem can generally be used if
The critical value for is
The corresponding confidence interval is computed as shown below:
Therefore, based on the data provided, the 95% confidence interval for the population mean is which indicates that we are 95% confident that the true population mean is contained by the interval