# Respond to normal distribution discussion with references | COUC 701 – Statistics | Liberty University

The normal distribution is a “continuous probability distribution that is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side.” (Mcleod, 2019) The area under the normal distribution curve represents probability and the total area under the curve sums to one. (Mcleod, 2019) The normal distribution has two parameters, the mean (μ) and the standard deviation (σ). Meaning that if there is a change in the standard deviation, it can cause a change in the shape of the normal curve and it can become fatter and wider or skinnier and taller depending on the change in standard deviation. Normal distribution is symmetrical and shaped a bit like a bell (Bell Curve). (Holmes, Illowsky & Dean, 2017)

The normal blood pressure for a healthy person is less than 120/80. (Heart.org, 2022) The systolic blood pressure in healthy adults has a normal distribution with mean 112 mmHg and standard deviation 10 mmHg. About 68.3% of healthy adults have systolic blood pressure between 102 and 122 mmHg. (Ane, 2006) However, blood pressure readings are affected by a variety of factors including stress levels, diet, duration and frequency of exercise. Some people will either have elevated blood pressures while others could have low blood pressures.

Height is another example of a variable that follows a normal distribution. The heights of adult men in the United States are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Heights of adult women are approximately normally distributed with a mean of 64.5 inches and a standard deviation of 2.5 inches. (Illustrative Mathematics, 2016)

The variable of blood pressure is likely to have a higher standard deviation since the range of blood pressure among the population can be large. Also, the normal distribution for systolic blood pressures has mean of 112 mmHg and standard deviation of 10 while the average normal distribution and standard deviation in both men and women is a lot lower.

References:

Ané, Cécile. “The Famous Bell Curve the Standard Normal 0 1 – University of Wisconsin …” The Normal Distribution, 2006, https://pages.stat.wisc.edu/~ane/st371/notes/chap4_by4.pdf.

Heart.org, Heart Association. “Understanding Blood Pressure Readings.” Www.heart.org, 5 Jan. 2022, https://www.heart.org/en/health-topics/high-blood-pressure/understanding-blood-pressure-readings.

Holmes, A., Illowsky, B., & Dean, S. (2017). Introductory business statistics. OpenStax.