Question

Bill Scott is a Project Manager at a real estate development company. The CEO requested a specific project to be completed in 185 days to satisfy certain loan requirements. The CEO asked Bill to generate the probabilities and statistics for the targeted completion date. Typical completion times (from start to finish) for this type of project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. The probability that this project will be completed in 185 or fewer work-days is ________. (Use the z table for this problem)

0.4332 0.0668 0.5000 0.9950 0.9332

Answer 1

Here, μ = 200, σ = 10 and x = 185. We need to compute P(X <= 185). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (185 - 200)/10 = -1.5

Therefore,
P(X <= 185) = P(z <= (185 - 200)/10)
= P(z <= -1.5)
= 0.0668

Option B