Single period profit/loss calculation

6 A factory makes loaves of bread in batches. One batch of loaves contains \(X\) kilograms of dried yeast and \(Y\) kilograms of flour, where \(X\) and \(Y\) have the independent distributions \(\mathrm { N } \left( 0.7,0.02 ^ { 2 } \right)\) and \(\mathrm { N } \left( 100.0,3.0 ^ { 2 } \right)\) respectively. Dried yeast costs \(
) 13.50\( per kilogram and flour costs \)\\( 0.90\) per kilogram. For making one batch of bread the total of all other costs is \(
) 55\(. The factory sells each batch of bread for \)\\( 200\). Find the probability that the profit made on one randomly chosen batch of bread is greater than \(
) 40$. [7]

5 A company uses two drivers for deliveries.
Driver \(A\) charges a fixed rate of \(\pounds 80\) per day plus \(\pounds 2\) per mile travelled on that day. Driver \(B\) charges a fixed rate of \(\pounds 120\) per day plus \(\pounds 1.50\) per mile travelled on that day.
On each working day the total distance, in miles, travelled by each driver is a random variable with the distribution \(\mathrm { N } ( 83,360 )\).

1. Find the probability that driver \(A\) charges the company less than \(\pounds 235.00\) for a randomly chosen day’s deliveries.
2. Find the probability that the total charge to the company of three randomly chosen days' deliveries by driver \(A\) is at least \(\pounds 300\) more than the total charge of two randomly chosen days' deliveries by driver \(B\).