CAIE S1 2013 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicBinomial Distribution
TypeIdentify distribution and parameters

5 Fiona uses her calculator to produce 12 random integers between 7 and 21 inclusive. The random variable \(X\) is the number of these 12 integers which are multiples of 5 .
  1. State the distribution of \(X\) and give its parameters.
  2. Calculate the probability that \(X\) is between 3 and 5 inclusive. Fiona now produces \(n\) random integers between 7 and 21 inclusive.
  3. Find the least possible value of \(n\) if the probability that none of these integers is a multiple of 5 is less than 0.01.