$-.10\mathrm{.}28$ Based on a careful work study in the Hofstetter Corp., the results shown in the following table have been observed:

$\backslash$table$[[$EIEMENT$,$OBSERVATIONS $($MINUTES$),$PERFORMANCE RATING $(\%)],[1,2,3,4,5],[$Prepare daily reports,$35,40,33,42,39,120],[$Photocopy results,$12,10,{36}^2,15,13,110],[$Label and package reports,$3,3,5,5,4,90],[$Distribute reports,$15,18,21,17,{45}^b,85]]$

a$)$ Compute the normal time for each work element.

b$)$ If the allowance for this type of work is $15\%,$ what is the standard time?

c$)$ How many observations are needed for a $95\%$ confidence level within $+-5\%$ accuracy? $($Hint: Calculate the sample size of each element.$)$