CAIE S1 2013 June — Question 4

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicBinomial Distribution
TypeFinding binomial parameters from properties

4 Robert uses his calculator to generate 5 random integers between 1 and 9 inclusive.
  1. Find the probability that at least 2 of the 5 integers are less than or equal to 4 . Robert now generates \(n\) random integers between 1 and 9 inclusive. The random variable \(X\) is the number of these \(n\) integers which are less than or equal to a certain integer \(k\) between 1 and 9 inclusive. It is given that the mean of \(X\) is 96 and the variance of \(X\) is 32 .
  2. Find the values of \(n\) and \(k\).