Explain or apply conditions in context

Questions that require explaining what specific conditions mean in the given context, commenting on validity of assumptions, or discussing whether conditions are likely to hold in a particular scenario.

27 questions

WJEC Unit 2 Specimen Q3
3. Cars arrive at random at a toll bridge at a mean rate of 15 per hour.
  1. Explain briefly why the Poisson distribution could be used to model the number of cars arriving in a particular time interval.
  2. Phil stands at the bridge for 20 minutes. Determine the probability that he sees exactly 6 cars arrive.
  3. Using the statistical tables provided, find the time interval (in minutes) for which the probability of more than 10 cars arriving is approximately 0.3 .
OCR Further Statistics 2021 June Q3
3 The numbers of CD players sold in a shop on three consecutive weekends were 7,6 and 2 . It may be assumed that sales of CD players occur randomly and that nobody buys more than one CD player at a time. The number of CD players sold on a randomly chosen weekend is denoted by \(X\).
  1. How appropriate is the Poisson distribution as a model for \(X\) ? Now assume that a Poisson distribution with mean 5 is an appropriate model for \(X\).
  2. Find
    1. \(\mathrm { P } ( X = 6 )\),
    2. \(\mathrm { P } ( X \geqslant 8 )\). The number of integrated sound systems sold in a weekend at the same shop can be assumed to have the distribution \(\operatorname { Po } ( 7.2 )\).
  3. Find the probability that on a randomly chosen weekend the total number of CD players and integrated sound systems sold is between 10 and 15 inclusive.
  4. State an assumption needed for your answer to part (c) to be valid.
  5. Give a reason why the assumption in part (d) may not be valid in practice.