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Applications of the Normal Distribution
QUESTION
Explain the Applications of the Normal Distribution
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Statistics |
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Answer
Fig 1: Histogram of the DX32 variable.
The variable does not exhibit a normal distribution (with even distribution around the mean) but a Pareto distribution, with uneven distribution as the class before the mean class had incomparable number of entries – this was influenced by the fact that most months did not have temperatures less than 32 degrees F (Arnold, 2014).
My random sample had a mean of 4.8, which is less than the 3.6 overall sample mean. If the variable was normally distributed, the expectation of getting mean close to 3.6 (within the confidence interval of the mean) is supported by the fact that the values of the variable are evenly distributed. Meaning that the mean across the entries would not differ from the population mean (which is estimated to always be within the confidence interval of the sample mean which is 3.6). Further, means of 100 samples from the DX32 variable would not depict normal distribution since the means only follow normal distribution if the population follows a normal distribution. When the distribution of the population is normal, then the distribution of the sample mean is also normal, therefore the truncated samples’ means would follow a normal distribution (Nadarajah, 2005). In this case, they would not because variable DX32 does not follow a normal distribution.
References
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Arnold, B. C. (2014). Pareto distribution. Wiley StatsRef: Statistics Reference Online, 1-10.
Nadarajah, S. (2005). A generalized normal distribution. Journal of Applied statistics, 32(7), 685-694.
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