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Perhaps a mistaken impression, after completing an initial course in statistics, is that one distribution is better than another. Many other distributions exists. Usually, introductory statistics classes concern confidence limits, hypothesis testing and sample size determination which all involve a sampling distribution of a particular statistic such as the mean. The normal distribution is often the appropriate distribution in these areas. The normal distribution is appropriate when the random variable in question is the result of many small independent random variables that have been are summed . The attached link shows this very well. Theoretically, a random variable approaches the normal distribution as the sample size tends towards infinity. (Central limit theory) As a practical matter, it is very important that the contributing variables be small and independent.
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What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
How do you check for normal distribution?
There are two main methods: theoretical and empirical. Theoretical: Is the random variable the sum (or mean) of a large number of imdependent, identically distributed variables? If so, by the Central Limit Theorem the variable in question is approximately normally distributed. Empirical: there are various goodness-of-fit tests. Two of the better known are the chi-square and the Kolmogorov-Smirnov tests. There are others. These compare the observed values with what might be expected if the distribution were Normal. The greater the discrepancy, the less likely it is that the distribution is Normal, the smaller the discrepancy the more likely that the distribution is Normal.
Why is A bell shaped probability distribution curve is NOT necessarily a normal distribution?
There are infinitely many sets of parameters that will generate a bell shaped curves - or near approximations. The Student's t or binomial, for large sample sizes get very close to the Gaussian distribution. There are others, too.
When data is normally distributed which test can be taken?
The answer depends on what is being tested: the t-test, F-test, Chi-square, Z-test are all commonly used with the Normal distribution. There are many others.
Definition of normal proportion of letters?
Oh, dude, you're asking about the normal distribution of letters in the English language! Basically, it's a fancy way of saying that certain letters show up more often than others in words. Like, 'E' is the popular kid on the block, while 'Z' is the loner sitting in the corner. So, if you're into letter popularity contests, this is the distribution for you.
