OCR S2 2009 January — Question 8

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2009
SessionJanuary
TopicApproximating Binomial to Normal Distribution
TypeJustify normal approximation

8 A sales office employs 21 representatives. Each day, for each representative, the probability that he or she achieves a sale is 0.7 , independently of other representatives. The total number of representatives who achieve a sale on any one day is denoted by \(K\).
  1. Using a suitable approximation (which should be justified), find \(\mathrm { P } ( K \geqslant 16 )\).
  2. Using a suitable approximation (which should be justified), find the probability that the mean of 36 observations of \(K\) is less than or equal to 14.0 . 4