123ArticleOnline Logo
Welcome to 123ArticleOnline.com!
ALL >> Others >> View Article

Applications Of The Normal Distribution

Profile Picture
By Author: allan
Total Articles: 366
Comment this article
Facebook ShareTwitter ShareGoogle+ ShareTwitter Share

Shop Replica Watches for men and ladies at Top-Watches-Brand.com. Search for fashion dress watches, luxury diamond watches or gold watches. The unique design and high quality of the Rolex replica watches has attracted many of its suporters worldwide.The normal distribution is very important in statistical inference. We should realize, however, that it is not a natural law that we encounter each time we analyze a continuous random variable. The normal distribution is a theoretical or ideal, distribution. No set of measurements conforms exactly to its specifications. Many sets of measurements, however, are approximately normally distributed. In such cases, the normal distribution is quite useful when we try to answer practical questions regarding these data.

In particular, whenever a set of measurements is approximately normally distributed, we can find the probability of occurrence of values within any specific interval, just as we can with the standard normal distribution. We can do this because we can ...
... easily transform any normal distribution with a known mean JJL and standard deviation CT to the standard normal distribution. Once we have made this transformation, we can use a table of standard normal areas to find relevant probabilities.

We can transform a normal distribution to the standard normal distribution using the formula z=(x- (JL)/CT. This transforms any value of x in an original distribution with mean) x and standard deviation CT to the corresponding value of z in the standard normal distribution.
The Normal Approximation to the Binomial
The normal distribution gives a good approximation to the binomial distribution when n is large and p is not too close to 0 or 1. This enables us to calculate probabilities for large binomial samples for which binomial tables are not available. A good rule of thumb is that the normal approximation to the binomial is appropriate when np and n(l - p) are both greater than 5. To normally distributed, we can make more powerful probability statements than we could fusing Chebyshev's theorem.

The normal distribution is completely determined by its parameters u, and cr. That is, each different value of JJL or o~ specifies a different normal distribution.

The Standard Normal Distribution

The normal distribution is really a family of distributions in which one member is distinguished from another on the basis of the values of |x and a. In other words, as already indicated, there is a different normal distribution for each different value of either |x or a.
The most important member of this family of distributions is the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We usually use the letter z for the random variable that results from the standard normal distribution. The probability that z lies between any two points on the z axis is determined by the area bounded by perpendiculars erected at each of these points, the curve, and the horizontal axis. We find areas under the curve of a continuous distribution by integrating the function between two values of the variable. There are tables that give the results of integrations in which we might be interested. The table of the standard normal distribution may be presented in many different forms.

Applications of the Normal Distribution

The normal distribution is very important in statistical inference. We should realize, however, that it is not a natural law that we encounter each time we analyze a continuous random variable. The normal distribution is a theoretical or ideal, distribution. No set of measurements conforms exactly to its specifications. Many sets of measurements, however, are approximately normally distributed. In such cases, the normal distribution is quite useful when we try to answer practical questions regarding these data.

In particular, whenever a set of measurements is approximately normally distributed, we can find the probability of occurrence of values within any specific interval, just as we can with the standard normal distribution. We can do this because we can easily transform any normal distribution with a known mean ju, and standard deviation a to the standard normal distribution.

Once we have made this transformation, we can use a table of standard normal areas to find relevant probabilities.
We can transform a normal distribution to the standard normal distribution using the formula z = (x- (x)/a. This transforms any value of x in an original distribution with mean u- and standard deviation CT to the corresponding value of z in the standard normal distribution.
The Normal Approximation to the Binomial

The normal distribution gives a good approximation to the binomial distribution when n is large and p is not too close to 0 or 1. This enables us to calculate probabilities for large binomial samples for which binomial tables are not available. We convert values of the original variable to values of z to find the probabilities of interest.

The Continuity Correction. The normal distribution is continuous and the binomial is discrete. Therefore we get better results if we make an adjustment to account for this when we use the approximation. The need for such an adjustment, called the continuity correction, is evident when we compare a histogram constructed from binomial data with a superimposed smooth curve.

Total Views: 305Word Count: 845See All articles From Author

Add Comment

Others Articles

1. Discover The Art Of Boutique Ceramic Products With House Of Ceramic
Author: Matthew Edwards

2. 5 Reasons To Buy Quality Crossbody Handbags
Author: BIBA HK

3. Weatherproofing Your Home With Terracotta Roof Repointing
Author: Richard Jones

4. Vashikaran Astrologer In Bijapur
Author: Astrology112

5. How To Create Safe Spaces For The Lgbtqia+ Community: A Guide To Inclusivity And Support
Author: Im Perfect by Urveez

6. Unlocking The Future Of Connectivity: The Power Of Low Power Mesh Networking
Author: ElaraTek

7. Why Saniquat Is A Game-changer In Cleaning And Disinfection
Author: New Wave Clean

8. The Timeless Value Of Photo Albums: Why They Matter
Author: HiTech Albums

9. Decoding Dyslexia: Lyla’s Story
Author: Im Perfect by Urveez

10. Understanding Ac Refrigerant Machines And Diagnostic Scanners: Essential Tools For Automotive Hvac Systems
Author: interequip

11. Best Astrologer In Jayanagar
Author: Srisaiastro1

12. Buying A Latex Mattress? Here Are Compelling Reasons To Say Yes
Author: Andrew Philips

13. Strategies To Maximize Your Results With Dental Seo Services
Author: dental SEO services

14. How Professional Furniture Removal Benefits The Environment
Author: Dave Kocemba

15. Room Makeover: Carpet Installation, Wooden Pergolas, And Kitchen Renovation Services In Auckland
Author: Onestop Trade

Login To Account
Login Email:
Password:
Forgot Password?
New User?
Sign Up Newsletter
Email Address: