MATH 1280 Discussion Unit6 PDF

Preview

Summary

MATH1280 Discussion Unit6...

Description

The normal distribution, also known as the Gaussian distribution or the bell curve, is an important probability distribution because it fits many natural phenomena (Frost, 2020). Before deciding whether to use the normal distribution, it's important to keep in mind its properties to determine if it is appropriate for the data:

It cannot be used to model data that is skewed. The mean, median, and mode must be one and the same. 50% of the population is measured at less than the mean and 50% is measured at higher. The Empirical Rule of 68%/95%/99.7% must be true. (Frost, 2020)

Researchers commonly use the normal distribution to model and approximate the probability of a random variable for things like blood pressure, birth weight, height of humans, shoe size, and IQ tests (MathIsFun, 2019). Even though the real distribution might vary from the model, the researcher can still use the normal distribution as an alternative to conducting a population study (at least for data generally agreed to follow the normal distribution). Stock traders sometimes try to fit stock price change data into a normal distribution but this is not an appropriate model because stock price data tends to be very skewed or have a high level of kurtosis (wide tails) which would not follow the Empirical Rule (Chen, 2020).

References: Chen, J. (2020, September 16). Normal Distribution. Investopedia. https://www.investopedia.com/terms/n/normaldistribution.asp.

Frost, J. (2020, September 2). Normal Distribution in Statistics. Statistics By Jim. https://statisticsbyjim.com/basics/normal-distribution/.

MathIsFun. (2019). Normal Distribution. Math is Fun. https://www.mathsisfun.com/data/standardnormal-distribution.html....