A methods and measurements analyst for Timepiece, Inc., needs to develop a time standard for the task of attaching a watch to a wristband. In a preliminary study, he observed one of his workers perform this task five times, with the following results: $$\begin{array} { l r r r r r }
\text { Observation } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Time (seconds) } & 27 & 19 & 20 & 21 & 13
\end{array}$$ What is the normal time for this task if the employee worked at a 20 percent faster pace than average?
A) 16.7 seconds
B) 20 seconds
C) 24 seconds
D) 25 seconds
E) 100 seconds

Question

A methods and measurements analyst for Timepiece, Inc., needs to develop a time standard for the task of attaching a watch to a wristband. In a preliminary study, he observed one of his workers perform this task five times, with the following results: $$\begin{array} { l r r r r r } 
\text { Observation } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Time (seconds) } & 27 & 19 & 20 & 21 & 13
\end{array}$$ What is the normal time for this task if the employee worked at a 20 percent faster pace than average?
A) 16.7 seconds
B) 20 seconds
C) 24 seconds
D) 25 seconds
E) 100 seconds

Quizplus · Accepted Answer

To find the normal time, we need to calculate the average time taken for the task. 
Sum of observations = $27+19+20+21+13=100$
Average time = $\dfrac{100}{5}=20$ seconds
If the employee works at a 20% faster pace than average, then the time taken by the employee is 80% of the normal time. 
Time taken by employee = $0.8 	imes 20=16$ seconds (rounded to nearest second)
However, the employee worked at a faster pace than this, i.e., 20% faster than the average pace. 
Time taken by employee = $0.8 	imes 20 \div 1.2 \approx 13.3$ seconds (rounded to nearest tenth)
So, the normal time for the task, at the average pace, is about 24 seconds (rounded to nearest second). 
Therefore, the best choice is C.