Question

For a given activity, the optimistic time, pessimistic time and the most probable time estimates are \(5\), \(17\) and \(8\) days respectively. The expected time is

• A. \(8\) days
• B. \(9\) days
• C. \(10\) days
• D. \(15\) days

Hint:

Remember the PERT formulas: \[ \boxed{t_e=\frac{t_o+4t_m+t_p}{6}} \] and \[ \boxed{\sigma^2=\left(\frac{t_p-t_o}{6}\right)^2.} \] The most probable time receives four times the weight in the expected time calculation.

Answer 1

The Correct Option is B

Concept: In PERT (Program Evaluation and Review Technique), the expected time of an activity is calculated using \[ \boxed{t_e=\frac{t_o+4t_m+t_p}{6}} \] where \[ t_o=\text{Optimistic time}, \] \[ t_m=\text{Most probable time}, \] and \[ t_p=\text{Pessimistic time}. \]

Step 1: Write the given data. \[ t_o=5\text{ days}, \] \[ t_m=8\text{ days}, \] \[ t_p=17\text{ days}. \]

Step 2: Apply the PERT formula. \[ t_e = \frac{5+4(8)+17}{6}. \] \[ = \frac{5+32+17}{6} = \frac{54}{6} = 9\text{ days}. \] Hence, \[ \boxed{t_e=9\text{ days}.} \] Therefore, the correct option is \[ \boxed{(B)\;9\text{ days}.} \]