Use this information for FIVE questions. We must reject $($A$1),$ further analyze $($A$2),$ or accept $($A$3)$ a lot of incoming material for quality improvement purposes. The payoff table is below. Based on historical data, there is $30\%$ chance that the lot is good quality $($ S $1),50\%$ chance that the lot is fair quality $($S$2),$ and $20\%$ chance that the lot is poor quality $($S$3).$

$\backslash$table$[[,S_1,S_2,S_3$