2025 Nov TZ3 P2 Q6

A garden centre sells seeds for two varieties of sunflowers: large and giant.
The heights of large sunflowers are normally distributed with mean \(\mu\) and standard deviation \(\sigma\).
It is known that \(25\%\) of large sunflowers have a height of over \(180\) cm.

1. Given that \(\mu + A\sigma = 180\), where \(A \in \mathbb{R}\), find the value of \(A\).

   [3]

The heights of giant sunflowers are also normally distributed.
The giant sunflowers have a mean height that is \(35\) cm more than that of the large sunflowers and a standard deviation that is double that of the large sunflowers.
It is known that \(98\%\) of giant sunflowers have a height greater than \(180\) cm.

2. Determine \(\mu\) and \(\sigma\).

   [4]