2025 MI P2 Q10

In this question you should state clearly all the distributions that you use, together with the values of the appropriate parameters.

In a fruit shop, the masses, in kg, of a certain type of apple and pear are modelled as having independent normal distributions with means and standard deviations as shown in the table.

1. An apple and a pear are chosen at random.
   1. Find the probability that the mass of the apple is more than \(0.25\) kg and the mass of the pear is less than \(0.25\) kg.[1]
   2. Find the probability that the mass of the apple is within \(0.075\) kg of the mass of the pear.[4]

Apples are sold at \(\$5\) per kg and pears at \(\$7\) per kg.

2. Find the probability that the total price of \(10\) randomly chosen apples and \(5\) randomly chosen pears exceeds \(\$22\).[4]