CAIE S1 2010 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeJustify normal approximation

5 In the holidays Martin spends \(25 \%\) of the day playing computer games. Martin's friend phones him once a day at a randomly chosen time.
  1. Find the probability that, in one holiday period of 8 days, there are exactly 2 days on which Martin is playing computer games when his friend phones.
  2. Another holiday period lasts for 12 days. State with a reason whether it is appropriate to use a normal approximation to find the probability that there are fewer than 7 days on which Martin is playing computer games when his friend phones.
  3. Find the probability that there are at least 13 days of a 40-day holiday period on which Martin is playing computer games when his friend phones.