Edexcel S2 2021 January — Question 3

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2021
SessionJanuary
TopicPoisson Distribution
TypeMultiple periods with binomial structure

3. The number of water fleas, in 100 ml of pond water, has a Poisson distribution with mean 7
  1. Find the probability that a sample of 100 ml of the pond water does not contain exactly 4 water fleas. Aja collects 5 separate samples, each of 100 ml , of the pond water.
  2. Find the probability that exactly 1 of these samples contains exactly 4 water fleas. Using a normal approximation, the probability that more than 3 water fleas will be found in a random sample of \(n \mathrm { ml }\) of the pond water is 0.9394 correct to 4 significant figures.
    1. Show that \(n - 1.55 \sqrt { \frac { n } { 0.07 } } - 50 = 0\)
    2. Hence find the value of \(n\) After the pond has been cleaned, the number of water fleas in a 100 ml random sample of the pond water is 15
  3. Using a suitable test, at the \(1 \%\) level of significance, assess whether or not there is evidence that the number of water fleas per 100 ml of the pond water has increased. State your hypotheses clearly. \includegraphics[max width=\textwidth, alt={}, center]{f63c39df-cfc9-4a6b-838d-67613710b0ce-11_2255_50_314_34}
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