Sampling Distribution of the Sample Means from an Infinite Population

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SUMMARY

The discussion focuses on the sampling distribution of sample means from an infinite population, specifically analyzing the scores of 84 students from a Trade School on a national test. The national test scores are normally distributed with a mean (μ) of 18.5 and a standard deviation (σ) of 7.8. For the sample of 84 students, the mean remains 18.5, while the standard deviation of the sample mean is calculated as σ/√n, resulting in approximately 0.85. The variance of the sample mean is determined to be 0.72.

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1. Individual students’ scores on a national test have a normal distribution with a mean of 18.5 and a standard deviation of 7.8. At a Trade School, 84 students took the test. If the scores at this school have the same distribution as national scores, what is the mean, standard deviation and variance of the sample mean for 84 students? Assume that in this case the population is infinite.
 
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If, out of a population large enough to be treated as infinite with mean $$\mu$$ and standard deviation [math]\sigma[/math], a sample of size n is taken we can expect the sample to have mean $$\mu$$ and standard deviation [math]\sigma \sqrt{n}[/math].
 

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