2018 TJC P2 Q7

A company manufactures tennis balls with radii that are normally distributed with mean \(3.3\) cm and standard deviation \(0.2\) cm.

1. Find the probability that the radius of a randomly selected tennis ball lies between \(3.135\) cm and \(3.465\) cm.
   Without any further calculation, explain with the aid of a diagram how the answer obtained would compare with the probability that the radius lies between \(3.465\) cm and \(3.795\) cm.[3]
2. \(3\) tennis balls are randomly selected. Find the probability that the largest tennis ball has radius less than \(3.4\)cm[2]

The tennis balls are packed into cylindrical tubes for sale. The cylindrical tubes have lengths that are normally distributed with mean \(20\) cm and standard deviation \(0.3\) cm. \(3\) tennis balls are randomly selected and packed into a randomly selected cylindrical tube such that the first tennis ball is in contact with the end of the tube and each subsequent ball is in contact with its neighbouring ball as shown in the diagram below.