The Central Limit Theorem (Essay Sample)

The Central Limit Theorem
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The Central Limit Theorem
Search methods; I google searched for the word the Central Limit Theorem, then researched further on its applicability in a practical set up.
The Central Limit Theorem dictates that if you have a sufficient number consisting of independent samples that are randomly selected, then ideally, the means of the samples used will follow the normal distribution  ADDIN EN.CITE Michael J. Glencross198661(Michael J. Glencross, 1986)616134Michael J. Glencross,A practical Approach to the Central Limit Theorem1986South AfricaUniversity of Witwaterstrand/~iase/publications/icots2/Glencross-1.pdf( HYPERLINK \l "_ENREF_1" \o "Michael J. Glencross, 1986 #61"
Michael J. Glencross, 1986).
A practical example of the Central Limit Theorem entails a case where a research company seeks to examine whether the results acquired on the mean salary of employees at eBay were by chance, or there were discrepancies. Ebay’s employees are known to have a mean salary of 9000, which translates to 26,000 and they also have a standard deviation of 2420. When a random sample of 400 employees is analyzed, their sample mean becomes 26,650. The Central Limit Theorem explains this practical example by saying that in instances where many groups are selected, approximately 400 individuals each, then the mean for each group is computed. The distribution of the means will be almost normal at 26, 400. At the same time, the standard deviation will be; σ/‚n = 2400 / ‚400 = 121.Therefore, how much z-score will a mean salary of 26,650 give?Z = data value – mean / standard deviation HYPER13 ADDIN EN.CITE Michael J. Glencross198661(Michael J. Glencross, 1986)616134Michael J. Glencross,A practical Approach to the Central Limit Theorem1986South AfricaUniversity of Witwaterstrand/~iase/publications/icots2/Glencross-1.pdf( HYPERLINK \l "_ENREF_1" \o "Michael J. Glencross, 1986 #61"
Michael J. Glencross, 1986).= 26,650 - 26400 / 121 = 2.07
The answer implies that in a case of ...