CAIE S1 2012 November — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2012
SessionNovember
TopicNormal Distribution
TypeRounded or discrete from continuous

5 The random variable \(X\) is such that \(X \sim \mathrm {~N} ( 82,126 )\).
  1. A value of \(X\) is chosen at random and rounded to the nearest whole number. Find the probability that this whole number is 84 .
  2. Five independent observations of \(X\) are taken. Find the probability that at most one of them is greater than 87.
  3. Find the value of \(k\) such that \(\mathrm { P } ( 87 < X < k ) = 0.3\).