CAIE S1 2002 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2002
SessionJune
TopicPermutations & Arrangements
TypeArrangements with adjacency requirements

5 The digits of the number 1223678 can be rearranged to give many different 7 -digit numbers. Find how many different 7-digit numbers can be made if
  1. there are no restrictions on the order of the digits,
  2. the digits 1,3,7 (in any order) are next to each other,
  3. these 7 -digit numbers are even.
  4. In a normal distribution with mean \(\mu\) and standard deviation \(\sigma , \mathrm { P } ( X > 3.6 ) = 0.5\) and \(\mathrm { P } ( X > 2.8 ) = 0.6554\). Write down the value of \(\mu\), and calculate the value of \(\sigma\).
  5. If four observations are taken at random from this distribution, find the probability that at least two observations are greater than 2.8.