Sampling from a normally distributed population.

What can we conclude when sampling from a normally distributed population? In other words, what can we conclude about samples drawn from a normally distributed population with mean equal to μ and standard deviation equal to σ ?

The followings hold true:

a. 

The mean of x̄ or μ is equal to the mean of the population or μ.

μx̄ = μ

The standard deviation of x̄ or σ is equal to σ/√n assuming of course n/N ≤ 0.05

$$ \sigma_{\overline{x}} = \frac{\sigma }{\sqrt{n} } $$

b. No matter what the value of n is, the shape of the sampling distribution of x̄ is also normally distributed.

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes