What is the basic purpose of employing work sampling techniques? What are the applications or uses of work sampling? $($ii$)$The following data were obtained during the course of the day to establish standard time for a lathe machine operation by means of work sampling: total number of observations $=150,$ number of observations operator idle $=50,$ average performance rating $=150\%,$ total time worked per day$=480$ min, number of pieces produced per day $=250$ pcs$.$ The company allows $5\%$ for personal, $5\%$ for unavoidable delays and $5\%$ for fatigue in establishing time standards. Determine the standard time in min.$/$pc$.($iii$)$ Assume that the work sampling study was continued for the second day and a total of $300$ observations were obtained, of these observations, the operator was found idle $75$ times. Determine the relative and absolute accuracies of operator idle time at a confidence level of $99\%.$