- The weights of bags of carrots, \(C \mathrm {~kg}\), are such that \(C \sim \mathrm {~N} \left( 1.2,0.03 ^ { 2 } \right)\)
Three bags of carrots are selected at random.
- Calculate the probability that their total weight is more than 3.5 kg .
The weights of bags of potatoes, \(R \mathrm {~kg}\), are such that \(R \sim \mathrm {~N} \left( 2.3,0.03 ^ { 2 } \right)\)
Two bags of potatoes are selected at random. - Calculate the probability that the difference in their weights is more than 0.05 kg .
The weights of trays, \(T \mathrm {~kg}\), are such that \(T \sim \mathrm {~N} \left( 2.5 , \sqrt { 0.1 } ^ { 2 } \right)\)
The random variable \(G\) represents the total weight, in kg, of a single tray packed with 10 bags of potatoes where \(G\) and \(T\) are independent. - Calculate \(\mathrm { P } ( G < 2 T + 20 )\)