CAIE S1 2024 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2024
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeSingle probability inequality

6 The residents of Mahjing were asked to classify their local bus service:
  • \(25 \%\) of residents classified their service as good.
  • \(60 \%\) of residents classified their service as satisfactory.
  • \(15 \%\) of residents classified their service as poor.
    1. A random sample of 110 residents of Mahjing is chosen.
Use a suitable approximation to find the probability that fewer than 22 residents classified their bus service as good.
  • For a random sample of 10 residents of Mahjing, find the probability that fewer than 8 classified their bus service as good or satisfactory.
  • Three residents of Mahjing are selected at random. Find the probability that one resident classified the bus service as good, one as satisfactory and one as poor.