Consider a project that has an expected completion time of 50 weeks and a standard deviation of 9 weeks.What is the probability that the project is finished in 57 weeks or fewer? (Round to two decimals. )
A)0.68
B)0.78
C)0.22
D)0.32
E)None of the above

Question

Quizplus · Accepted Answer

First, we need to normalize the distribution by using the formula:

Z = (X - mu) / sigma

where X is the completion time we are interested in (in this case, 57 weeks), mu is the expected completion time (50 weeks), and sigma is the standard deviation (9 weeks).

Z = (57 - 50) / 9 = 0.78

Next, we need to find the area under the normal distribution curve to the left of this Z-score using a standard normal distribution table or calculator. This area represents the probability that the project is finished in 57 weeks or fewer.

From the standard normal distribution table, we find that the area to the left of Z = 0.78 is 0.7794. Rounding to two decimal places, we get:

0.7794 ≈ 0.78

Therefore, the probability that the project is finished in 57 weeks or fewer is 0.78 or 78%. The best choice(s) that matches this answer is (B).

Consider a Project That Has an Expected Completion Time of 50