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CHAPTER $7$ The Normal and Other Continuous Distributions

In preparation for a meeting with the Depot commander, Dave decides to review data on lean improvement events. He finds that of the past $137$ projects, $30\%$ went beyond $60$ days. The commander suggests that Dave be "creative" in his presentation of the statistics to make it look like the group is actually in compliance with the DOD.

The completion times are yery skewed to the high end, which doesn't surprise Qave in the least. After all, no project can take less than $0$ time, but a few always seem to go on for a much longer time than planned. He is pleased to find that the average completion time is only $40$ days and that the standard deviation is $10$ days. Dave knows that a Normal model is a poor representation

of the completion times because of the skewness, but decides to use a $N(40,10)$ model. With this model, only about $2\mathrm{.}5\%$ of the projects would be expected to take more than $60$ days!

He explains his model to this supervisor who is pleased with the results. Even though they know the data don't fit the model well, they also know that the DOD analysts are very familiar with Normal models and will be pleased to know that they are in compliance using it$.$

Identify the ethical dilemma in this scenario.

What are the undesirable consequences?

Propose an ethical solution that considers the welfare of all stakeholders.