Normal Distribution - Introduction

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University of Minnesota, Duluth *

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Statistics

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Feb 20, 2024

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docx

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Normal Distribution: The normal distribution is a bell-shaped curve. You can draw the curve if you know the mean and the standard deviation. It is symmetric around the mean. If the mean is zero and the standard deviation is 1, then, the distribution is called a Standard Normal Distribution. Every normal distribution can be transformed to a standard normal distribution and vice versa. We would work with standard normal distribution first. Please see the diagram of the standard normal distribution below. To calculate probabilities, we would use the Excel function for the standard normal distribution, NORM.S.DIST(z,Cumulative). Here z denotes the value of the standard normal distribution and NORM.S.DIST(z,Cumulative) provides the cumulative probability for value z if we choose Cumulative=1 in this formula. For example, if you enter =NORM.S.DIST(-3,1) in a cell, the value would be .001349898 or .1% as shown in the graph below. Similarly, if you enter =NORM.S.DIST(-2.5,1) in a cell, the value would be .006209665 or .6%. Thus, the probability of getting a value between -3 and -2.5 would be the difference of the two, i.e., .006209665 - .001349898 - .004859767 or .5% as shown in the diagram below. Chart prepared by the NY State Education Department
Source: http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm , accessed May 8, 2012. Calculations for Normal Distribution are similar. As you know, Standard Normal Distribution (denoted by z) is a normal distribution with mean 0 and σ =1. Thus, you can use the formula for normal distribution, i.e., for z value between -3 and -2.5 could be calculated as follows: =norm.dist(-2.5,0,1,1)-norm.dist(-3,0,1,1) and you would get the same answer.
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