the uses of the normal distribution and the application of the Empirical Rule as well as the Central Limit Theorem

Normal Distribution, Empirical Rule, and Central Limit Theorem
Name
Institution
Normal Distribution, Empirical Rule, and Central Limit Theorem
Iron Levels in a Population
Mean = 15.5 gdL
Standard deviation = 1.6 gdL
Single Patient
Based on the empirical rule, 68% of the data values will fall ±1 SD of the mean. To calculate the values;
15.5 − 1.6 = 13.9
15.5 + 1.6 = 17.1
The range of numbers is 13.9 to 17.1
Next, 95% of the data values fall ±2 SD of the mean. The values are;
15.5 – 2(1.6) = 12.3
15.5 + 2(1.6) = 18.7
The range of numbers is 12.3 to 18.7
Finally, 99.7% of the data values will fall ±3 SD of the mean. They are;
15.5 – 3(1.6) = 10.7
15.5 + 3(1.6) = 20.3
The range of numbers is 10.7 to 20.3
Group of individuals
Sample size = 10
Using Central Limit Theorem,
Sample mean = 15
Standard Deviation = 0.32
Using empirical rule,
68% of the data values will fall ±1 SD of the mean. To calculate the values;
15 − 0.32 = 14.68
15 + 0.32 = 15.32
The range of numbers is 14.68 to 15.32
Next, 95% of the data values fall ±2 SD of the mean. The values are;
15 – 2(0.32) = 14.36
15 + 2(0.32) = 15.64
The range of numbers is 14.36 to 15.64
Finally, 99.7% of the data values will fall ±3 SD of the mean. They are;
15 – 3(0.32) = 14.04
15 + 3(0.32) = 15.96
The range of numbers is 14.04 to 15.96
Variables or measures that would probably follow a normal distribution.
The distribution of height and weight in the general population. The normal distribution is due to the Central Limit Theorem, which asserts that values that are a result of multiple small instances that are not too correlated results in that form of distribution (Barron, 1986).

For instance, height is determined by several genes, nutrition, and many other independent factors.

References
Barron, A. R. (1986). Entropy and the central limit theorem. The Annals of Probability, 336-342.