CAIE S1 2013 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicNormal Distribution
TypeFinding unknown boundaries

3 Buildings in a certain city centre are classified by height as tall, medium or short. The heights can be modelled by a normal distribution with mean 50 metres and standard deviation 16 metres. Buildings with a height of more than 70 metres are classified as tall.
  1. Find the probability that a building chosen at random is classified as tall.
  2. The rest of the buildings are classified as medium and short in such a way that there are twice as many medium buildings as there are short ones. Find the height below which buildings are classified as short.