# Probability Calculation for Normal Distribution

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Assuming that you have a data set that follows normal distribution, give examples of how you could use probability distribution to make predictions for the outcome of some business processes.

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Determine the process capability (Cp, Cpk), defects per million (DPM), and/or Z value of the normal distribution to the acceptable specification limits.

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• Predicting how long it will take to get reimbursement on expenses
• Predicting how long it will take to disposition requests for information

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Some thoughts I have:

1) knowing what the process is likely to deliver within an expected range allows us to better assess risk or opportunity to improve upon performance, or to distinguish ourselves from our competitors.  I'm thinking specifically about the advantages due to predictable lead times and the ability to deliver products quickly, and consistently meet customer expectations.

2) second, knowing what the process mean is relative to the desired nominal provides insight into improvement actions, whether adjusting the process performance to reduce the gap between the mean and a desired target, or reducing the process variation.  Different approaches may apply to the different desired improvement targets.

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Assuming a standard normal distribution , you can use probability distributions to make predictions for outcomes of business processes by:

1. calculating the area under the curve that does not meet the business limits - defining how far away from the limit the process is (Z value). With known X=0, sd=1, and a limit
2. calculating the  probability of the process not achieving or achieving the desired limits (DPMO) With known mean, sd, and limit
3. with known Z value (item 1) can convert to DPMO
4. with known DPMO (item 2) can convert to Z-value

Using the information to establish the business case and support the charter of a DMAIC to ensure we exceed the business goals.

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An airline has the normally distributed data of the price of jet fuel/barrel for each year of the past 20 years. The airline can use this data to anticipate how much jet fuel will cost for a specific time of year and adjust their ticket prices accordingly. They can also use this data to change their purchasing strategy on jet fuel futures as to beat the market.

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The data set follows a normal distribution and therefore can be characterized by the sample mean and standard distribution (S) with an associated confidence interval.  The process outcomes will follow this characterized distribution. For example, future data sets of comparable quantity will have a mean in the range of the confidence interval.

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Probability can be used to predict cycle, completion, response, and delay times.  It can also be used to predict how much rework or repair may be needed.  This can be used in planning and estimation activities.

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Prediction of warranty costs

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