- A company produces bricks.
The weight of a brick, \(B \mathrm {~kg}\), is such that \(B \sim \mathrm {~N} \left( 1.96 , \sqrt { 0.003 } ^ { 2 } \right)\)
Two bricks are chosen at random.
- Find the probability that the difference in weight of the 2 bricks is greater than 0.1 kg
A random sample of \(n\) bricks is to be taken.
- Find the minimum sample size such that the probability of the sample mean being greater than 2 is less than 1\%
The bricks are randomly selected and stacked on pallets.
The weight of an empty pallet, \(E \mathrm {~kg}\), is such that \(E \sim \mathrm {~N} \left( 21.8 , \sqrt { 0.6 } ^ { 2 } \right)\)
The random variable \(M\) represents the total weight of a pallet stacked with 500 bricks.
The random variable \(T\) represents the total weight of a container of cement.
Given that \(T\) is independent of \(M\) and that \(T \sim \mathrm {~N} \left( 774 , \sqrt { 1.8 } ^ { 2 } \right)\) - calculate \(\mathrm { P } ( 4 T > 100 + 3 M )\)