T T06-02 Normal & Standard Normal Templates Purpose T06-02 is an all in one template combining the features of the two templates T06-02.N and T06-02.S allowing the analyst to analyze the Normal and Standard Normal Probability Distribution. Probability Scenario's are calculated for "between", "greater than", and "less than" eliminating the need to perform calculations to use Standard Normal Distribution Tables. The template also allows the analyst to determine an X/Z value depending upon a "Cumulative Probability". A graphical representation of the Probability Scenario is also shown. Inputs Mean & Standard Deviation Normal or Standard Normal Distribution Probability Scenario Outputs Probability Scenario Solution Graph of Probability Scenario

T Normal Distribution A normal probability distribution describes many random processes or continuous phenomena. It is the basis for classical statistical inference. f ( X )=Frequency of random variable x  =Population standard deviation  = ; e = x =Value of random variable (-  < x <  )  =Population mean

T Standard Normal Distribution A normal probability distribution describes many random processes or continuous phenomena. It is the basis for classical statistical inference. f ( X )=Frequency of random variable x  =Population standard deviation =1  = ; e = x =Value of random variable (-  < x <  )  =Population mean = 0

T Battery Example A manufacturer of batteries claims that the average length of life for its grade A batteries is 60 months. Suppose the standard deviation of the life-length is 10 months and the frequency distribution of the life-length data is normally distributed. What is the probability that the batteries last a. Less than 52 months b. More than 82 months c. Between 42 and 77 months d. Determine the battery life such that the probability less than the battery life is equal to.8400?

T The Normal Distribution mean and standard deviation are entered here. Probability scenarios are automatically calculated after X values are entered. Normal Distribution worksheet tab

T Normal & Standard Normal Distribution This template allows you to calculate both Normal & Standard Normal Distribution scenarios. The previous slide shows the worksheet tab that for the template which calculates the Normal Probability Distribution scenarios. However, sometimes you may wish to calculate Standard Normal Probability Distribution scenarios. In this case there are two options: One: You can use 0 and 1 as the mean and standard deviation in the Normal Probability Distribution Two: You can use the second worksheet tab Standard Normal shown on the next slide The example demonstrates the Normal situation; however, the Standard Normal situation works the same way.

T Probability scenarios are automatically calculated after Z values are entered. Standard Normal Distribution worksheet tab

T What is the probability that the batteries last a. Less than 52 months Normal Distribution - Battery Example

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T The EXCEL Template also provides a Normal Distribution Graph showing the Probability Scenario.

T What is the probability that the batteries last b. More than 82 months Normal Distribution - Battery Example

T The EXCEL Template calculates these answers much quicker than looking them up in a table.

T The EXCEL Template also provides a Normal Distribution Graph showing the Probability Scenario.

T What is the probability that the batteries last c. Between 42 and 77 months Normal Distribution - Battery Example

T The EXCEL Template calculates these answers much quicker than looking them up in a table.

T The EXCEL Template also provides a Normal Distribution Graph showing the Probability Scenario.

T Normal Distribution - Battery Example Determine the battery life such that the probability less than the battery life is equal to.8400? In other words, What is the value of X such that CP(X) <=.8400?

T The EXCEL Template calculates these answers much quicker than looking them up in a table. Caution : In using this portion of the template, you must enter the problem such that the input is the Cumulative Probability.

T The EXCEL Template also provides a Normal Distribution Graph showing the Probability Scenario.