CAIE Further Paper 4 2023 November — Question 2

Exam BoardCAIE
ModuleFurther Paper 4 (Further Paper 4)
Year2023
SessionNovember
TopicChi-squared distribution

2 The number of breakdowns on a particular section of road is recorded each day over a period of 90 days. It is suggested that the number of breakdowns follows a Poisson distribution with mean 3.5. The data is summarised in the table, together with some of the expected frequencies resulting from the suggested Poisson distribution.
Number of breakdowns per day012345678 or more
Observed frequency0513172116954
Expected frequency2.7189.51216.64616.99311.8953.4692.407
  1. Complete the table.
  2. Carry out a goodness of fit test, at the 10\% significance level, to determine whether or not \(\operatorname { Po } ( 3.5 )\) is a good fit to the data.