CAIE S1 2024 November — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2024
SessionNovember
TopicNormal Distribution
TypeStandard two probabilities given

6 The heights of the female students at Breven college are normally distributed:
  • \(90 \%\) of the female students have heights less than 182.7 cm .
  • \(40 \%\) of the female students have heights less than 162.5 cm .
    1. Find the mean and the standard deviation of the heights of the female students at Breven college.
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Ten female students are chosen at random from those at Breven college.
  • Find the probability that fewer than 8 of these 10 students have heights more than 162.5 cm .