
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 29th, 2016, 07:27 AM  #1 
Newbie Joined: Feb 2016 From: Norway Posts: 2 Thanks: 0  Normal distribution: a probability distribution?
Hi! My professor said that we were going to look at different probability distributions and that the normal distribution is one of them. But in our textbook it says that the probability distribution will resemble the normal distribution graph when the sample is large enough. If this is right, it does not make much sense to me that the normal distribution IS a probability distribution. Does anyone know what is right? If so, may you explain? 
February 29th, 2016, 08:43 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
The normal distribution is a probability distribution because it describes the probability that a random variable X will fall within some range. For example, you can evaluate P(Z > 0) to be 0.5, P(1 < Z < 1) to be 0.68, and so on. You seem to be confused by the Central Limit Theorem, which purports that as the number of samples you take from any underlying distribution tends to infinity, the sample mean will tend to the normal distribution. That's true, but it doesn't mean that normal distributions only exist under sampling. It also appears everywhere from test scores to children's heights. I suggest you study and understand the normal distribution as a probability distribution first, then look at the Central Limit Theorem when you deal with statistical inference. 
February 29th, 2016, 11:49 AM  #3 
Newbie Joined: Feb 2016 From: Norway Posts: 2 Thanks: 0 
Thank you so much for your answer! I'm so grateful. I think I finally got the hang of it, or at least a better understanding.

February 29th, 2016, 04:35 PM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,969 Thanks: 807 
What your professor is saying is the 'law of large numbers' that essentially says that all probability distributions approach the normal probability distribution for sufficiently large number of trials. But that does not mean that it is not itself a probability distribution!


Tags 
distribution, normal, probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Probability question involving the normal distribution.  Statistics132  Advanced Statistics  2  June 20th, 2015 01:54 AM 
Joint Probability Density Function of a Sample of A Normal Distribution  IndependentThinker  Advanced Statistics  1  February 27th, 2015 02:01 PM 
Multivariate normal distribution and marginal distribution  nakys  Advanced Statistics  0  October 3rd, 2013 08:27 AM 
probability and standard normal distribution  agcliff09  Advanced Statistics  3  November 11th, 2007 10:37 AM 
Normal Distribution  symmetry  Advanced Statistics  1  April 18th, 2007 04:53 PM 