Question

Let x stand for the percentage of an individual student's math test score. 100 students were sampled at a time. The population mean is 75 percent and the population standard deviation is 12 percent. What are the mean and standard deviation of the sampling distribution of sample means?

Answer 1

The mean of the sampling distribution of sample means is 75 percent, equal to the population mean. The standard deviation, known as the standard error, is 1.2 percent, which is the population standard deviation (12 percent) divided by the square root of the sample size (100).

Step-by-step explanation:

When considering the sampling distribution of sample means with a population mean of 75 percent and a population standard deviation of 12 percent for samples of size 100, we can apply the central limit theorem to calculate the mean and standard deviation of the sampling distribution. The mean (μx) of the sampling distribution is equal to the population mean (μ), which, in this case, is 75 percent.

The standard deviation (σx) of the sampling distribution, also known as the standard error, is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n). So, it would be σx = σ / √n = 12% / √100 = 12% / 10 = 1.2 percent. Therefore, the standard deviation of the sampling distribution of sample means for samples of size 100 is 1.2 percent.