An activity has four elements. The activity is work$-$measured and the times $(r)$ are recorded on continuous basis over five cycles. The observations are given in table :

$\backslash$table$[[$Work Element,Observations,Rating factor$],[$Cycle $1,2,3,4,5],[1,0\mathrm{.}50,3\mathrm{.}30,5\mathrm{.}70,8\mathrm{.}20,10\mathrm{.}85,1\mathrm{.}1],[2,0\mathrm{.}70,3\mathrm{.}45,5\mathrm{.}95,8\mathrm{.}55,11\mathrm{.}10,1\mathrm{.}2],[3,1\mathrm{.}45,4\mathrm{.}05,6\mathrm{.}50,9\mathrm{.}25,11\mathrm{.}75,1\mathrm{.}2],[4,2\mathrm{.}75,5\mathrm{.}25,7\mathrm{.}60,10\mathrm{.}35,13\mathrm{.}05,0\mathrm{.}9]]$

The time $r$ is recorded at the end of work$-$element.

$($i$)$ Calculate: $($a$)$ Normal time of the activity, $($b$)$ Standard time for the activity, if the allowance is $20\%.$

$($ii$)$ What is the appropriate sample size for estimating the time for element $2$ within $-10\%$ of the true mean with $95\%$ confidence; the standard deviation for the time for element $2$ is $0\mathrm{.}0742.$