CAIE S1 2023 November — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionNovember
TopicNormal Distribution
TypeMixed calculations with boundaries

3 A farmer sells eggs. The weights, in grams, of the eggs can be modelled by a normal distribution with mean 80.5 and standard deviation 6.6. Eggs are classified as small, medium or large according to their weight. A small egg weighs less than 76 grams and \(40 \%\) of the eggs are classified as medium.
  1. Find the percentage of eggs that are classified as small.
  2. Find the least possible weight of an egg classified as large.
    150 of the eggs for sale last week were weighed.
  3. Use an approximation to find the probability that more than 68 of these eggs were classified as medium.