Math Problem Statement

A population of values has a normal distribution with and . You intend to draw a random sample of size .

What is the mean of the distribution of sample means?

What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)

Solution

To answer your question about the distribution of sample means, we'll use the properties of the normal distribution.

  1. Mean of the Distribution of Sample Means: The mean of the distribution of sample means (also known as the sampling distribution) is equal to the mean of the population. If the population mean is denoted as μ\mu, then the mean of the sample means is also μ\mu.

  2. Standard Deviation of the Distribution of Sample Means: The standard deviation of the distribution of sample means, also known as the standard error (SE), is calculated using the formula: SE=σn\text{SE} = \frac{\sigma}{\sqrt{n}} where σ\sigma is the standard deviation of the population and nn is the sample size.

To provide specific numerical answers, please supply the population mean (μ\mu), the population standard deviation (σ\sigma), and the sample size (nn).

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Sampling Distribution
Central Limit Theorem

Formulas

Mean of the sampling distribution: μ
Standard deviation of the sampling distribution (Standard Error): σ / √n

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12