The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Use Table B and Table B1.

Path	Expected Duration (weeks)		Variance
A	10		1.21
B	8		2.00
C	12		1.00
D	15		2.89
E	14		1.44

Click here for the Excel Data File

Assuming the project begins now, what is the probability that the project will be completed before: (Round your z-value to 2 decimal places and all intermediate probabilities to 4 decimal places. Round your final answers to 4 decimal places.) a. Graduation time?

b. The end of week 15?

c. The end of week 13?