$*($i$)$Why are performance rating and allowance so critical and controversial in stop$-$watch time study? What approaches may be taken to alleviate the problems of performance rating and allowances in industry?

$($ii$)$ In a stop$-$watch time study, the following information is provided for a given work element: number of readings$=25,$ mean element time$=0\mathrm{.}20$ min, standard deviation$=0\mathrm{.}06$ min.

$($a$)$ Calculate the range of elemental time values at a confidence level of $95\%$ and the percentage of the accuracy level.

$($b$)$ Suppose it is desired in the above problem that the mean elemental time should be within the accuracy level of $10\%$ with a confidence level of $95\%.$ Determine the number of observations or readings that must be taken to achieve this