$9.$ Data from an $8-$h work sampling study are shown below. a$.$ What percentage of the time is the machine running? b$.$ What percentage of the time is the machine broken? c$.$ What is the limit of accuracy of this study for a$50\mathrm{.}05?$ d$.$ What is the $95$ percent confidence interval of the machine running? e$.$ Your manager says that the range in part d is unacceptably large. She would like to narrow the range down to $61$ min of running time. How many observations should you collect to achieve this?