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Every year, more than 100,000 test-takers take the Law School Admission Test (LSAT). One year, the scores had a mean of approximately 151 points and a standard deviation of 9 points. Suppose that in the scoring process, test officials audit random samples of 36 tests. Calculate the mean and standard deviation of the sampling distribution of the sample mean.

Answer :

Final answer:

The mean of the sampling distribution of the sample mean is 151, the same as the population mean. The standard deviation of the sampling distribution, or standard error, is 1.5 points.

Explanation:

When officials audit random samples of 36 tests from the LSAT, they are engaging in the process of understanding the sampling distribution of the sample mean. The mean of the sampling distribution will be the same as the population mean, so it remains at 151. The standard deviation of the sampling distribution, also known as the standard error, will be the population standard deviation divided by the square root of the sample size (n).

Therefore, the standard deviation of the sampling distribution is calculated as 9 / √36 which equals 1.5 points

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