Standard percentage calculations

Questions that only require finding percentages/proportions for given boundary values using direct normal distribution calculations, without needing to find unknown boundaries.

1 questions

CAIE S1 2020 June Q4
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.