Percentage of a normal population below a value and a design height from an upper percentile plus a fixed clearance

The heights of the adults who use a city's railway are normally distributed with mean \(169.5\) cm and standard deviation \(7.5\) cm.

1. Find the percentage of these adults who are shorter than \(158\) cm.[3]
2. The railway's new carriages are built so that \(98\%\) of these adults, standing upright inside a carriage, have a gap of at least \(15\) cm between the top of the head and the ceiling. Find the height of the ceiling, correct to the nearest centimetre.[4]