Posted by Jason L on Friday, March 2, 2007 at 8:31am.
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 guarentee a completion date. If the job is not done in a specified number of hours the contracter 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.
You can use z-scores and the z-score formula to compute the number of hours.
Formula: z = (x - mean)/sd -->sd = standard deviation
You are given the mean and standard deviation. You can find z using a z-table representing "no more than 6% risk" of having to pay up. Once you have that z-score, all you will need to do is solve the above equation for x.
I hope this will help get you started.
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