CAIE S1 2024 June — Question 2

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2024
SessionJune
TopicNormal Distribution
TypeDirect comparison of probabilities

2 In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m .
  1. Find the probability that an adult chosen at random from this country will have height greater than 1.93 m .
    \includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-04_2716_35_143_2012}
    \includegraphics[max width=\textwidth, alt={}, center]{9b21cc0f-b043-4251-8aa9-cb1e5c2fb5d0-05_2724_35_136_20} In another country, the heights of the adult population are also normally distributed. \(33 \%\) of the adult population have height less than \(1.56 \mathrm {~m} .25 \%\) of the adult population have height greater than 1.86 m .
  2. Find the mean and the standard deviation of this distribution.