Suppose that the standard deviation of the tube life of a particular brand of TV picture
tube is known to be 500, the population of tube life cannot be assumed to be normally
distributed. However, the sample mean of x = 8900 is based on a sample of n = 35.
Construct the 95% confidence interval for estimating the population mean.
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
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