Question

A population of values has a normal distribution with μ = 136 and σ = 32.1 . You intend to draw a random sample of size n = 167 . What is the mean of the distribution of sample means? μ ¯ x = What

Answer 1

The mean of the sampling distribution of the sample mean is equal to the population mean, which is 136, according to the Central Limit Theorem.

Step-by-step explanation:

The mean of the distribution of sample means (often referred to as the expected value of the sample mean or the mean of the sampling distribution) is equal to the population mean. In other words, if you draw multiple random samples from a population and calculate the mean of each sample, the average of those sample means will be equal to the population mean.

So, in this case, the mean of the distribution of sample means (X) is equal to the population mean (μ): X = μ

Therefore, the mean of the distribution of sample means is 136.