For an activity, the estimates for optimistic, pessimistic and most likely times are 2, 12 and 5 days. The expected time and variance of this activity are

Concept:

The PERT (Project Evaluation and Review Technique) technique is used, when activity time estimates are stochastic in nature. For each activity, three values of time (optimistic, most likely, pessimistic) are estimated.

• Optimistic time (to) estimate is the shortest possible time required for the completion of the activity
• Most likely time (tm) estimate is the time required for the completion of activity under normal circumstances
• Pessimistic time (tp) estimate is the longest possible time required for the completion of the activity

In PERT expected time of an activity is determined by using the below-given formula:

\({t_e} = \frac{{\left( {{t_o} + 4{t_m} + {t_p}} \right)}}{6}\)

Variance, σ2 = \({\left[ {\frac{{{t_P} - {t_0}}}{6}} \right]^2}\)

Calculation:

t_o = 2, t_p = 12, and t_m = 5

Expected time

\({{\text{t}}_{\text{E}}}=\frac{{{\text{t}}_{\text{o}}}+4{{\text{t}}_{\text{m}}}+{{\text{t}}_{\text{p}}}}{6}=\frac{2+4\left( 5 \right)+12}{6}=5.7\text{ }\!\!~\!\!\text{ days}\)

Variance, σ2 = \({\left[ {\frac{{{t_P} - {t_0}}}{6}} \right]^2}\) = \({\left[ {\frac{{{12} - {2}}}{6}} \right]^2}\)= 2.8
Note: In official paper the given options are not match with correct values, so we updated the option 1.