This section shows how to compute these approximations. Since this is a non-mathematical treatment of statistics, we will rely on computer programs and tables to determine these areas. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
This demonstration allows you to explore the accuracy of the approximation under a variety of conditions. Critics have said that extreme events in reality are more frequent than would be expected assuming normality.
The assumption has even been called a "Great Intellectual Fraud. E: Normal Distribution Exercises. For example, the Z-Score of 2. The benefit of Standardization is that with the help of a Z-Score table we can easily calculate exact areas for any given normally distributed population with any mean or standard deviation and it also enables us to compare two scores that are from different samples which may have different means and standard deviations.
The values that are less than mean zero , correspond to a negative score in Z-Table and lie to the left of the mean as observed in the figure above. Similarly, the values that are greater than mean zero , make positive score in Z-Table and lie to the right of the mean on graph. What proportion of students score less than To map the same on the Z-Table, we need to choose the respective Z-Table negative or positive based on whether our Z Score is negative or positive. In our case, the Z Score is To find area under the curve for After that we need to run alongside the X-axis of topmost row to find the value of digits at the second decimal position 0.
Now map these two values on the Z-table and find the intersection of the row of first two digits and column of the second decimal value in table. And voila! Example 2: The test score of 50 students in a class is normally distributed with mean 65 and a standard deviation of 8.
What proportion of students score more than The most important thing to understand when calculating area under the curve to the right of Z-Score is,. The credits for the discovery of the normal distribution are not unanimous. Some authors attribute the credit to Abraham de Moivre and some authors attribute the credit to Carl Friedrich Gauss.
Hence, the normal distribution has also been interchangeably known as the Gaussian Distribution over the years. Pierre-Simon Laplace is also credited with making significant contributions to the normal distribution since he was the first to pose the problem of aggregating observations. However, it led him to crafting his own double exponential distribution as a solution which is known as the Laplacian distribution.
It was also Laplace and not Gauss who proved the central limit theorem, which acts as a theoretical base to the normal distribution. Right from the coining of the normal distribution, it has been known by various different names. Following were the names interchangeably used for the normal distribution to name a few:.
However, on the left hand side of CLT we get. Then, using the definition of continuous distribution function. But since. There is an alternate not a pure mathematical derivation of the Gaussian PDF which uses Information Theoretic arguments, the idea there is briefly this: Let X be a continuous r.
This is one of the reasons why communication engineers are fond of the Gaussian r. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How was the normal distribution derived? Ask Question. Asked 8 years, 6 months ago.
Active 8 months ago. Viewed 49k times. D 5, 1 1 gold badge 16 16 silver badges 41 41 bronze badges. Cisplatin Cisplatin 4, 6 6 gold badges 29 29 silver badges 53 53 bronze badges. Show 2 more comments. Active Oldest Votes. Let's make two assumptions about the way I play darts.
PS a factor of two seems to be wrong in my derivation but I have to go to the airport now. Tim Tim 5, 19 19 silver badges 31 31 bronze badges. The exponential has this characteristic but why is it the only one to have it? Show 4 more comments. Sam Gallagher Sam Gallagher 3 3 silver badges 10 10 bronze badges.
Doesn't the square root still have to be a part of g? It's still there, but moved into the undetermined function. Show 6 more comments.
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