Final answer:
The correct answers are options A and B. When random samples of size 36 are drawn from a population with a mean of 20 and a standard deviation of 9, the mean of the sampling distribution remains 20, and the standard deviation becomes 1.5, which is the standard error.
Step-by-step explanation:
The student's question deals with the concept of sampling distribution of the sample means. When we draw random samples of a certain size from a population with a known mean and standard deviation, the distribution of the sample means itself has a mean equal to the population mean (Central Limit Theorem) and its standard deviation is equal to the population standard deviation divided by the square root of the sample size, known as the standard error.
The correct options that describe the mean and standard deviation of the sampling distribution of the sample means are:
A) The mean of the x distribution is 20. This is because the sampling distribution’s mean is always equal to the population mean.
B) The standard deviation of the x distribution is 9. Since the sample size n = 36, the standard error (the standard deviation of the mean of the x distribution) would be the population standard deviation (9) divided by the square root of the sample size (6), which equals 1.5.