CAIE S2 2021 November — Question 1

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2021
SessionNovember
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TopicCentral limit theorem
1 It is known that the height \(H\), in metres, of trees of a certain kind has the distribution \(\mathrm { N } ( 12.5,10.24 )\). A scientist takes a random sample of 25 trees of this kind and finds the sample mean, \(\bar { H }\), of the heights.
  1. State the distribution of \(\bar { H }\), giving the values of any parameters.
  2. Find \(\mathrm { P } ( 12 < \bar { H } < 13 )\).
1 It is known that the height $H$, in metres, of trees of a certain kind has the distribution $\mathrm { N } ( 12.5,10.24 )$. A scientist takes a random sample of 25 trees of this kind and finds the sample mean, $\bar { H }$, of the heights.\\
(a) State the distribution of $\bar { H }$, giving the values of any parameters.\\

(b) Find $\mathrm { P } ( 12 < \bar { H } < 13 )$.\\

\hfill \mbox{\textit{CAIE S2 2021 Q1}}
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