OCR MEI S1 2013 June — Question 3

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
Year2013
SessionJune
TopicBinomial Distribution
TypeNested binomial expected count

3 The weights of bags of a particular brand of flour are quoted as 1.5 kg . In fact, on average \(10 \%\) of bags are underweight.
  1. Find the probability that, in a random sample of 50 bags, there are exactly 5 bags which are underweight.
  2. Bags are randomly chosen and packed into boxes of 20 . Find the probability that there is at least one underweight bag in a box.
  3. A crate contains 48 boxes. Find the expected number of boxes in the crate which contain at least one underweight bag.