OCR S2 2007 January — Question 5

Exam BoardOCR
ModuleS2 (Statistics 2)
Year2007
SessionJanuary
TopicApproximating the Binomial to the Poisson distribution
TypeBinomial of Poisson approximations

5 On a particular night, the number of shooting stars seen per minute can be modelled by the distribution \(\operatorname { Po(0.2). }\)
  1. Find the probability that, in a given 6 -minute period, fewer than 2 shooting stars are seen.
  2. Find the probability that, in 20 periods of 6 minutes each, the number of periods in which fewer than 2 shooting stars are seen is exactly 13 .
  3. Use a suitable approximation to find the probability that, in a given 2-hour period, fewer than 30 shooting stars are seen.