A high definition television manufacturer in Asia wants to develop a new smart television as fast as possible using Program Evaluation and Review Technique (PERT) and must complete the design and testing work first. The objective is to be the first to market the most innovative smart television on the planet and capture the first adopter market share. The manufacturer has determined the following activities, precedence relationships, and time estimates in days for the project:
$\begin{array}{rcccr}& \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \
\text { Activity } & \text { Predecessors } & t_{o} & t_{m} & t_{p}\\hline
a & \text { none } & 4 & 6 & 7 \
\mathrm{~b} & \mathrm{a} & 1 & 2 & 3 \
\mathrm{c} & \mathrm{a} & 5 & 5 & 5 \
\mathrm{~d} & \mathrm{~b} & 7 & 9 & 12 \
\mathrm{e} & \mathrm{b} & 2 & 4 & 8 \
\mathrm{f} & \mathrm{c} d & 6 & 9 & 10
\end{array}$ Solutions are at the end of questions
-The standard deviation (not variance) of the critical path in days is _____.
A) less than or equal to 1.0 days
B) greater than 1.0 but less than or equal to 2.0 days
C) greater than 2.0 but less than or equal to 3.0 days
D) greater than 3.0 days

Question

A high definition television manufacturer in Asia wants to develop a new smart television as fast as possible using Program Evaluation and Review Technique (PERT) and must complete the design and testing work first. The objective is to be the first to market the most innovative smart television on the planet and capture the first adopter market share. The manufacturer has determined the following activities, precedence relationships, and time estimates in days for the project:
 $\begin{array}{rcccr}& \text { Immediate } & \text { Optimistic } & \text { Most Likely } & \text { Pessimistic } \
\text { Activity } & \text { Predecessors } & t_{o} & t_{m} & t_{p}\\hline
a & \text { none } & 4 & 6 & 7 \
\mathrm{~b} & \mathrm{a} & 1 & 2 & 3 \
\mathrm{c} & \mathrm{a} & 5 & 5 & 5 \
\mathrm{~d} & \mathrm{~b} & 7 & 9 & 12 \
\mathrm{e} & \mathrm{b} & 2 & 4 & 8 \
\mathrm{f} & \mathrm{c} d & 6 & 9 & 10
\end{array}$ Solutions are at the end of questions 
-The standard deviation (not variance) of the critical path in days is _____.
A) less than or equal to 1.0 days
B) greater than 1.0 but less than or equal to 2.0 days
C) greater than 2.0 but less than or equal to 3.0 days
D) greater than 3.0 days

Quizplus · Accepted Answer

The critical path is a-b-d-f. The standard deviation for each activity is calculated using $(t_p - t_o)/6$. For a-b-d-f, the standard deviations are 0.5, 0.33, 0.83, and 0.67 respectively. The standard deviation of the critical path is the square root of the sum of the variances: $\sqrt{0.5^2 + 0.33^2 + 0.83^2 + 0.67^2} \approx 1.16$, which is greater than 1.0 but less than or equal to 2.0 days.

A High Definition Television Manufacturer in Asia Wants to Develop