CAIE S1 2023 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2023
SessionJune
TopicNormal Distribution
TypeFind p then binomial probability

6 The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On \(10 \%\) of days less than 16 kg of grapes are sold.
  1. Find the standard deviation of the mass of grapes sold per day.
    The mass of grapes sold on any day is independent of the mass sold on any other day.
  2. 12 days are chosen at random. Find the probability that less than 16 kg of grapes are sold on more than 2 of these 12 days.
  3. In a random sample of 365 days, on how many days would you expect the mass of grapes sold to be within 1.3 standard deviations of the mean?