$1.$ A Methods and Measurements Analyst needs to develop a time standard for a certain task. In a preliminary study, one employee was observed performing this task five times, with the following results:OBSERVATIONTIME $($SECONDS$)184276380484576$a$)$ What is the Observed Time $($OT$)$ for his task? $($Answer$-80$ seconds$)$What is the normal time $($NT$)$ for this task if the employee worked at a twenty$-$five percent faster pace than the average? $\{$Answer$=(80)(1\mathrm{.}25)=100$ seconds;c$)$ What is the standard time $($ST$)$ for this task if the employee worked at a twenty$-$five percent faster pace than the average and an allowance of twenty percent of job time is used? $\{$Answer$=(80)(1\mathrm{.}25)($AF$),$ were AF$=1\mathrm{.}20$; ST$=(100)(1\mathrm{.}2)=120$ seconds$\}$d$)$ What is the standard time $($ST$)$ for this task if the employee worked at a twenty$-$five percent faster pace than the average and an allowance of twenty percent of the workday is used? $\{$Answer$=(80)(1\mathrm{.}25)($AF$),$ where AF$=1/(1-0\mathrm{.}20)$; ST$=(100)/(0\mathrm{.}8)=125$ seconds;How many observations should be made if the analyst wants to be $99\mathrm{.}74$ percent confident that the maximum error in the observed time is twe seconds? Assume that the standard deviation of task times is $4$ seconds. $($Answer: n $=($zs$)/($e$)?,$ where we are using the margin of sampling error directly to estimate n; z$-$Approx. $3$ for a two$-$tailed test of significance for the normal distribution, $\text{'}$s$\text{'}($sample standard deviation$-$ with $4$ observations$-$we are following the definition of the unbiased sample variance, e$=2$ seconds; Answer: n$=$Approx. $36$ observations$)$