Edexcel S2 2016 January — Question 5

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2016
SessionJanuary
TopicPoisson Distribution
TypePoisson parameter from given probability

5. The number of eruptions of a volcano in a 10 year period is modelled by a Poisson distribution with mean 1
  1. Find the probability that this volcano erupts at least once in each of 2 randomly selected 10 year periods.
  2. Find the probability that this volcano does not erupt in a randomly selected 20 year period. The probability that this volcano erupts exactly 4 times in a randomly selected \(w\) year period is 0.0443 to 3 significant figures.
  3. Use the tables to find the value of \(w\) A scientist claims that the mean number of eruptions of this volcano in a 10 year period is more than 1 She selects a 100 year period at random in order to test her claim.
  4. State the null hypothesis for this test.
  5. Determine the critical region for the test at the \(5 \%\) level of significance.