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Every year, more than 100,000 testers 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.

[tex]\mu_{\bar{x}} = \text{_____ points}[/tex]

Answer :

Final answer:

The mean of the sampling distribution of sample mean is 151 points and the standard deviation is 1.5 points.

Explanation:

To calculate the mean and standard deviation of the sampling distribution of sample mean, we can use the following formulas:

Mean of sampling distribution (μx) = Mean of population (μ)

Standard deviation of sampling distribution (σx) = Standard deviation of population (σ) / √Sample size (n)

For this question, the mean of the population is 151 points and the standard deviation is 9 points. The sample size is 36. Plugging these values into the formula, we get:

μx = 151 points

σx = 9 points / √36

= 9 / 6

= 1.5 points

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