Taking soil samples and testing the soil properties takes an engineer an average
ID: 2932201 • Letter: T
Question
Taking soil samples and testing the soil properties takes an engineer an average of 35.5 days per project. The duration varies because of differences in the soil, site terrain, and site location, and the variability of the engineer’s productivity. The duration follows a normal distribution with a standard deviation of 1.9 days. When asked how long it will take the engineer to do the work on the next project, the engineer feels optimistic and says “34 days”.
a. What is the probability that the work will be completed within this duration?
b. What is the probability that the work will take longer than this duration?
c. What duration should the engineer say to ensure with 95% confidence that the duration will not be exceeded?
d. If the engineer wanted to increase the confidence level that the duration would not be exceeded, what could they do?
Explanation / Answer
(a) P(X<34) = P[Z = (34-35.5)/1.9]
= P(Z = -1.5/1.9)
= P(Z = 0.7894)
= 0.785061
(b) P(X>34)
= 1 - P[Z = (34-35.5)/1.9]
= 1 - 0.785061
= 0.214939
(c) Z at 95% confidence = 1.96
Duration = [35.5 - 1.96 * 1.9 , 35.5 + 1.96 * 1.9]
= [35.5 - 3.724 , 35.5 + 3.724]
= [31.776 , 39.224]
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