Problem $1$

The continuous timing method in direct time study was used to obtain the elements. Elements $($ a $)(2$ ?minutes $)$ ?and Element $($ b $)(4$ ?minutes $)$ ?are operator controlled and external to the machine cycle, and they were performance rated at $80\%.$ ?Element $($ c $)(3$ ?minutes $)$ ?is a machine $-$ controlled element and the time is constant. If the machine cycle allowance is $10\%,$ ?and the worker PFD allowance is $15\%,$ ?determine $($ a $)$ ?the normal time, $($ b $)$ ?the standard time for the cycle. $)$

Problem $2$

Nine cycles have been observed during a direct time study. The mean for the largest element time is $1\mathrm{.}0$ ?minutes, and the corresponding sample standard deviation is $0\mathrm{.}12$ ?minute, which was also the largest. If the analyst wants to be $95\%$ ?confident that the mean of the sample was within $\frac{+}{-}0\mathrm{.}10\%$ ?of the true mean many more observations should be taken.