CAIE S1 2015 June — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeNormal approximation to normal-derived binomial

5 The heights of books in a library, in cm, have a normal distribution with mean 21.7 and standard deviation 6.5. A book with a height of more than 29 cm is classified as 'large'.
  1. Find the probability that, of 8 books chosen at random, fewer than 2 books are classified as large.
  2. \(n\) books are chosen at random. The probability of there being at least 1 large book is more than 0.98 . Find the least possible value of \(n\).