CAIE S1 2020 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2020
SessionJune
TopicNormal Distribution
TypeStandard percentage calculations

4 Trees in the Redian forest are classified as tall, medium or short, according to their height. The heights can be modelled by a normal distribution with mean 40 m and standard deviation 12 m . Trees with a height of less than 25 m are classified as short.
  1. Find the probability that a randomly chosen tree is classified as short.
    Of the trees that are classified as tall or medium, one third are tall and two thirds are medium.
  2. Show that the probability that a randomly chosen tree is classified as tall is 0.298 , correct to 3 decimal places.
  3. Find the height above which trees are classified as tall.