Completion time (from start to finish)of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days.To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days.
A)211
B)207
C)223
D)200
E)250

Question

Quizplus · Accepted Answer

To be 99% sure of not being late, we need to find the z-score corresponding to the upper tail of the normal distribution that captures 99% of the data. The z-score for 99% confidence is approximately 2.33 (you can find this value in z-tables or statistical software). Using the formula for converting z-scores to raw scores: X = μ + zσ, where X is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values: X = 200 + 2.33(10) = 200 + 23.3 = 223.3. Rounding to the nearest whole number gives 223 work-days.

Completion Time (From Start to Finish)of a Building Remodeling Project