# theoretical distribution

• Sep 30th 2007, 08:03 PM
rmweeks
theoretical distribution
Let X denote the length in millimeters of an organism. Assume that this variable X is Normally distributed with mean 12.2 and standard deviation 5.6. Let X denote the sample mean length for any random sample of four organisms.
What is the (theoretical) distribution of all such X's?

They give us a page of different sized organisms...im thinking this means i have to measure all of them or 4 of them
• Sep 30th 2007, 08:12 PM
CaptainBlack
Quote:

Originally Posted by rmweeks
Let X denote the length in millimeters of an organism. Assume that this variable X is Normally distributed with mean 12.2 and standard deviation 5.6. Let X denote the sample mean length for any random sample of four organisms.
What is the (theoretical) distribution of all such X's?

They give us a page of different sized organisms...im thinking this means i have to measure all of them or 4 of them

The distribution of sample means of samples of size N drawn from a normal distribution N(mu, sigma^2) is:

N(mu,sigma^2 / N),

so in this case X is normally distributed with mean 12.2 and SD 5.6/2 = 2.8.

RonL