Understanding Normal Distribution Notation: N(mu,alpha) vs. Z~N(mu,alpha)

In summary, N(mu,alpha) notation represents a normal distribution with a mean of mu and a standard deviation of alpha. Z~N(mu,alpha) and X~N(mu,alpha) are both used to denote a random variable with a normal distribution, but Z specifically indicates a standard normal distribution. The notation N(_,_) cannot be used for a non-normal distribution.
  • #1
zmike
139
0
I am a bit confused with the notation, Whenever I see N(mu,alpha) does that mean the data set is normal and does it also mean that it's standard normal?

Is there a difference between using Z~N(mu,alpha) vs. X~N(mu,alpha)? does the Z indicate standard normal?, if so why don't we just use Z(mu,alpha)?Can I still use this notation N(_,_) when the data set is NOT normal?

THANKS IN ADVANCE :D
 
Last edited:
Physics news on Phys.org
  • #2
Standard notation: X~N(m,d) means X is a random variable, with a normal distribution having a mean m and standard deviation d. If you wrote Z(m,d) then you need to define Z. N(m,d) means the distribution is normal - you can't use it for something else - it is a matter of notation.

If d is unknown for a normal distribution with a known m, then, as you observed, you can specify the midpoint of the distribution, but nothing else.
 

What is a normal distribution?

A normal distribution, also known as a Gaussian distribution, is a type of probability distribution that is commonly found in nature. It is a bell-shaped curve that is symmetrical around the mean, with most data points falling near the mean and fewer data points falling further away from the mean.

What are the characteristics of a normal distribution?

The characteristics of a normal distribution include a symmetrical shape, a single peak at the mean, and a bell-shaped curve. It also follows the 68-95-99.7 rule, where approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Why is the normal distribution important?

The normal distribution is important because it is a very common distribution in nature and can be used to model many real-world phenomena. It also allows us to make predictions and calculate probabilities based on the data we have.

How is the normal distribution related to the central limit theorem?

The central limit theorem states that, as the sample size increases, the sampling distribution of the sample means will approach a normal distribution regardless of the underlying distribution of the population. This means that even if the population does not follow a normal distribution, the sample means will still follow a normal distribution.

How do you calculate probabilities using the normal distribution?

To calculate probabilities using the normal distribution, you can use the standard normal distribution table or a statistical software. You will need to know the mean and standard deviation of the data, as well as the desired probability or area under the curve. You can then use the z-score formula or the cumulative distribution function to calculate the probability.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
341
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
815
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
981
  • Set Theory, Logic, Probability, Statistics
Replies
30
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
338
Replies
13
Views
525
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
  • Introductory Physics Homework Help
3
Replies
95
Views
3K
Back
Top