CAIE S1 2014 November — Question 5

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionNovember
TopicBinomial Distribution
TypeNested binomial expected count

5 Screws are sold in packets of 15. Faulty screws occur randomly. A large number of packets are tested for faulty screws and the mean number of faulty screws per packet is found to be 1.2 .
  1. Show that the variance of the number of faulty screws in a packet is 1.104 .
  2. Find the probability that a packet contains at most 2 faulty screws. Damien buys 8 packets of screws at random.
  3. Find the probability that there are exactly 7 packets in which there is at least 1 faulty screw.