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### Statistical Projections

The kind of problem that is laid out before us is a typical one in the world of business and is thus (at least to some extent) amenable to statistical analysis. Given that statistics is designed to deal with the unknown, and that much of what goes into a good business is being able to make contingency plans to compensate for unknowns, statistical analysis can often meet the needs of business owners.

The question at hand here is the time and therefore the expense involved in painting a room.

The room is eight feet by ten feet by eight feet. This results in a room that is 640 square feet. In fact, it is somewhat smaller than this in terms of total square feet because of the door and the windows, but the time taken to mask these compensates almost exactly for the time it would take to paint them, so the area is something of a wash. If we remove the footage for the ceiling and for the floor, the area is 480 square feet.

One person can paint 100 square feet of indoor wall space each hour, with a standard deviation of 12 square feet. On average the time required for an individual to paint this room would therefore be six hours and forty minutes. We would therefore expect two-thirds of all painters (given this standard deviation normally distributed) to take between approximately two hours and thirty-four minutes and approximately three hours and sixteen minutes. If the painter starts to work at 2 p.m., in two-thirds of the cases he or she will finish between 4:34 p.m. and 6:16 p.m. Any painter falling outside of a single deviation of the norm in this case would incur overtime.

It is impossible to determine from the facts presented whether or not the painter can receive any additional money because we do not know the terms of the contract. Given that the range (considering one standard deviation) of painting times at its bottom is still over two hours, it is unlikely that any more than one third of painters could make a better pro...

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