Exercise $3$

A certain work operation consisting of four elements has been subjected to a stopwatch time study. Table Q$5$ shows the time study data obtained for each of the task elements. Based on the company's policy, the allowances for tasks are personal $10\%,$ fatigue $10\%$ and delay $5\%.$

Table Q$5$: Time study data

$\backslash$table$[[$Task Element,Observation $($minutes$),\backslash$table$[[$Rerformance$],[$Rating $(\%)]]],[,1,2,3,4,5],[$A$,-,3\mathrm{.}0,2\mathrm{.}9,2\mathrm{.}8,2\mathrm{.}7,70],[$B$,7\mathrm{.}1,7\mathrm{.}3,7\mathrm{.}4,7\mathrm{.}5,7\mathrm{.}0,90],[$C$,2\mathrm{.}2,2\mathrm{.}1,2\mathrm{.}3,-,3\mathrm{.}4,110],[$D$,1\mathrm{.}1,1\mathrm{.}2,1\mathrm{.}1,1\mathrm{.}2,2\mathrm{.}5,120]]$

i$.$ Compute the standard time.

ii$.$ From the observation, the task performed by one worker produced the following sample time $($in minutes$)$; $3\mathrm{.}9,3\mathrm{.}2,3\mathrm{.}5,4\mathrm{.}1$ and $3\mathrm{.}6.$ How many observations would be necessary to determine the true cycle time with confidence level of $95\%(z$ value $1\mathrm{.}96)$ and an accuracy of $+-5\%?$