Problem

A string of length 40 cm is cut into 2 pieces at a random point.

The continuous random variable $L$ represents the length of the longer piece of string.

(a) Write down the distribution of $L$

(b) Find the probability that the length of the longer piece of string is 28 cm to the nearest cm.

Each piece of string is used to form the perimeter of a square.

(c) Calculate the probability that the area of the larger square is less than $64 \text{ cm}^2$

(d) Calculate the probability that the difference in area between the two squares is greater than $81 \text{ cm}^2$

(Total for Question 5 is 11 marks)