Standard +0.3 This is a straightforward application of linear combinations of normal random variables. Students need to recognize that the sum of 6 independent N(40.4, 5.2²) variables follows N(6×40.4, 6×5.2²), then calculate P(Sum < 220) using standardization. It's a direct textbook exercise requiring only routine application of formulas with no problem-solving insight needed, making it slightly easier than average.
1 The masses, in grams, of plums of a certain type have the distribution \(\mathrm { N } \left( 40.4,5.2 ^ { 2 } \right)\). The plums are packed in bags, with each bag containing 6 randomly chosen plums. If the total weight of the plums in a bag is less than 220 g the bag is rejected.
Find the percentage of bags that are rejected.
1 The masses, in grams, of plums of a certain type have the distribution $\mathrm { N } \left( 40.4,5.2 ^ { 2 } \right)$. The plums are packed in bags, with each bag containing 6 randomly chosen plums. If the total weight of the plums in a bag is less than 220 g the bag is rejected.
Find the percentage of bags that are rejected.\\
\hfill \mbox{\textit{CAIE S2 2020 Q1 [4]}}