CAIE S1 2009 November — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2009
SessionNovember
TopicNormal Distribution
TypeIndependent events across days/trials

7 The weights, \(X\) grams, of bars of soap are normally distributed with mean 125 grams and standard deviation 4.2 grams.
  1. Find the probability that a randomly chosen bar of soap weighs more than 128 grams.
  2. Find the value of \(k\) such that \(\mathrm { P } ( k < X < 128 ) = 0.7465\).
  3. Five bars of soap are chosen at random. Find the probability that more than two of the bars each weigh more than 128 grams.