MHB Sampling Distribution of the Sample Means from an Infinite Population

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The individual scores on a national test are normally distributed with a mean of 18.5 and a standard deviation of 7.8. For a sample of 84 students from this population, the mean of the sample mean remains 18.5. The standard deviation of the sample mean is calculated as 7.8 divided by the square root of 84, resulting in approximately 0.85. The variance of the sample mean is the square of the standard deviation, which is about 0.72. This analysis confirms that the sample mean retains the population mean while its variability decreases with larger sample sizes.
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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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