OCR MEI Further Statistics Major 2024 June — Question 2

Exam BoardOCR MEI
ModuleFurther Statistics Major (Further Statistics Major)
Year2024
SessionJune
TopicPoisson Distribution
TypePoisson parameter from given probability

2 The number of cars arriving per minute to queue at a drive-through fast-food restaurant is modelled by the random variable \(X\). The standard deviation of \(X\) is 0.6 . You should assume that arrivals are random and independent and occur at a constant average rate.
  1. Find the mean of \(X\).
    1. Calculate \(\mathrm { P } ( X = 1 )\).
    2. Calculate \(\mathrm { P } ( X > 1 )\).
  2. Find the probability that fewer than 5 cars arrive in a randomly chosen 20 -minute period.