Preliminary research resulted in the estimate that 30% of the employee group's time is consumed cataloguing. How many work sampling observations would have to be made if we wanted to have 95% confidence that the observed data were within a +- 10% tolerance of the population data? The following table illustrates some of the data they collect about 6 of the 20 employees. From this data they determine a standard in hours of 100 items. NOTE: all the elements are included in the total observations The number of volumes cataloged is equal to 14,612. design a control chart based on 3 limits for daily observations Travel time 15 min

\begin{tabular}{|l|r|r|r|r|r|r|} \hline Tiempo de horas trabajadas & 78 & 80 & 80 & 65 & 72 & 75 \\ \hline Total de observaciones & 152 & 170 & 181 & 114 & 143 & 158 \\ \hline Observaciones que implican catalogacin & 50 & 55 & 48 & 29 & 40 & 55 \\ \hline Evaluacin media & 90 & 95 & 105 & 85 & 90 & 100 \\ \hline \end{tabular} \begin{tabular}{|l|r|r|r|r|r|r|} \hline Tiempo de horas trabajadas & 78 & 80 & 80 & 65 & 72 & 75 \\ \hline Total de observaciones & 152 & 170 & 181 & 114 & 143 & 158 \\ \hline Observaciones que implican catalogacin & 50 & 55 & 48 & 29 & 40 & 55 \\ \hline Evaluacin media & 90 & 95 & 105 & 85 & 90 & 100 \\ \hline \end{tabular}