38) Activity Z has estimates a = 5, b = 12, m = 7; activity X has estimates a = 5, b = 11, m = 6; and activity Y has estimates a = 3, b = 11, m = 8. Which of the following statements is BEST? A) Activity X is longer than Activity Y. B) Activity X has a higher standard deviation than Activity Z. C) Activity Z is shorter than Activity Y. D) Activity Y has a smaller variance than Activity Z.

# Brief Explanations:<br />To determine which statement is best, we need to calculate the expected duration for each activity. The formula for the expected duration of an activity using PERT (Project Evaluation and Review Technique) is given by \(E(T) = \frac{a+4m+b}{6}\). Calculating for each:<br /><br />- For Activity Z:<br /> \(E(T) = \frac{5 + 4(7) + 12}{6} = 8\)<br /><br />- For Activity X:<br /> \(E(T) = \frac{5 + 4(6) + 11}{6} = 7.67\)<br /><br />- For Activity Y:<br /> \(E(T) = \frac{3 + 4(8) + 11}{6} = 8.33\)<br /><br />Comparing the expected durations, Activity Z (8) is shorter than Activity Y (8.33).<br /><br /># Answer:<br />C) Activity Z is shorter than Activity Y.