Question

A normal distributed population has parameters μ=250 and σ=25.2. If a random sample of size n=34 is selected,

a. What is the mean of the distribution of sample means? μ_x = [Answer box]
b. What is the standard deviation of the distribution of sample means? Round to two decimal places. σ_x = [Answer box]

Answer 1

The mean of the distribution of sample means is equal to the population mean, 250. The standard deviation of the distribution of sample means, or standard error, is the population standard deviation divided by the square root of the sample size and should be rounded to two decimal places.

Step-by-step explanation:

The question is about finding the mean and standard deviation of a sampling distribution when the population parameters are known.

The population has a mean (μ) of 250 and a standard deviation (σ) of 25.2. Given that the sample size (n) is 34, we can determine the following:

1. The mean of the distribution of sample means, also known as the expected value of the sample mean (μx), will be equal to the population mean (μ), which is 250.
2. The standard deviation of the distribution of sample means, also called the standard error of the mean (σx), is calculated using the formula σx = σ/√n. Plugging in the values gives us σx = 25.2 / √34.
3. After calculation, it should be rounded to two decimal places.

We will use the Central Limit Theorem to justify the use of the population standard deviation in the formula for the standard deviation of the sample means.