9709 P52 - Jun 2026 - Q7 - 9 marks
9176
The lengths of the leaves of a certain type of tree are normally distributed with mean \(\mu\) cm and standard deviation \(\sigma\) cm. It is known that 20% of the leaves have a length less than 3.60 cm and 70% of the leaves have a length greater than 5.40 cm.
(a) Find the value of \(\mu\) and the value of \(\sigma\). [5]
The lengths of 600 randomly chosen leaves of a different type of tree are normally distributed with mean 4.63 cm and standard deviation 0.55 cm.
(b) How many of these 600 leaves would you expect to have a length within 0.6 cm of the mean length? [4]
