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.

Question

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.

Answer 1

To determine the number of hours the contractor should guarantee for completion with no more than a 6% risk, we need to find the Z-score corresponding to the highest 6% of completion times.

The formula to calculate the Z-score is: Z = (X - μ) / σ

Where:
Z is the Z-score,
X is the desired completion time (in hours),
μ is the mean completion time (in hours),
σ is the standard deviation of completion times (in hours).

Since we are only concerned with one side of the normal distribution, we want to find the Z-score for the 94th percentile (100% - 6% = 94%).

Using a Z-score table or a Z-score calculator, we can find that the Z-score for the 94th percentile is approximately 1.555.

Now we can rearrange the Z-score formula to solve for X:

X = Z * σ + μ

Substituting the known values:

X = 1.555 * 5 + 40

X ≈ 47.775

Therefore, the contractor should guarantee completion within approximately 47.775 hours to take no more than a 6% risk of having to pay up.

Remember, this calculation assumes that completion times follow a normal distribution and that the contractor wants to guarantee completion within the highest 6% of completion times.