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A building contractor claims that they can renovate a 200 sq foot kitchen and dining room in 40 work hours plus minus 5 (the mean and standard deviation respectively). The work includes plumbing, electrical installation, cabinets, flooring, painting and installing new appliances. From past experience we assume that times to complete similar projects are normally distributed. In order to gain a competitive edge the contractor wishes to guarantee a completion date. If the job is not done in a specified number of hours the contractor will reimburse 20% of the total cost to the owner. What should the number of hours be if they wish to take no more than a 6% risk of having to pay up? Advice - Draw the key elements of the solution before you compute.

Here you are only concerned with one side of the normal distribution, the highest 6%. Use your Z-score formula again. See other posts.

I hope this helps. Thanks for asking.

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