Compare and Contrast of Normal and Standard Distribution Discussion example

Compare and Contrast of Normal and Standard Distribution Discussion

Question: Compare and contrast the normal distribution with the standard distribution. Give practical examples of each and provide the analysis with each example.

A normal distribution could be determined by the parameters of the variance and the mean. In statistics, people refer to normal distribution in case when they are collecting data from the normal distribution in order
of stimulation of these parameters. The standard normal distribution is specific with a mean of 0 and a variance 1. Such distribution could be used for a construction of tables of the normal distribution. If X would have a
normal distribution with a mean of m and a variance of s2 , we may define

Z= X-m ÷ s

Z as a value that has a standard distribution. That is why, for any of the specific distribution that is normal, it can be possible to calculate some probabilities of the form P [a write X=sZ+m. The standard distribution is playing a role respecting to the general family of the normal distributions (Marsaglia, 2014).

Practical example for standard distribution may be a possibility to count friends in the same school within a condition if one of them is 1,85 m tall than the others. It could be seen that

1.85 m is a standard deviation from the meaning of 1.4, that is why a height of a friend has “z-score” on a number of 3.0. It is possible to calculate a number of standard deviations 1.85 from the mean of “How far
may be 1.85 from the mean?”. It will be 1.85-1.4 = 0.45 from a mean. The standard deviation would be 0.15 m, that is why 0.45m/0.15 m = 3 deviations (Walker, 2015).

Example on normal distribution may be represented in a task where 95% of the students at school would be between 1.1. m and 1.7 m of tall. If to assume such data that is normally distributed, the normal deviation would
be calculated. Mean = (1.1m = 1/7 m)/2 =1.4 m. In this case, 95% would be considered as either side of mean deviations, where 1 normal deviation would be (1.7 m – 1.1 m)/4 =0.6m/4=0.15m.

References

Marsaglia, George; Tsang, Wai Wan (2014). "The Ziggurat Method for Generating Random Variables". Journal of Statistical Software. 5 (8).
Walker, Helen (2015). Studies in the History of the Statistical Method. Baltimore, MD: Williams & Wilkins Co. pp. …