OCR FS1 AS 2018 March — Question 2

Exam BoardOCR
ModuleFS1 AS (Further Statistics 1 AS)
Year2018
SessionMarch
TopicContinuous Uniform Random Variables
TypeFind parameters from given statistics

2 The number of calls received by a customer service department in 30 minutes is denoted by \(W\). It is known that \(\mathrm { E } ( W ) = 6.5\).
  1. It is given that \(W\) has a Poisson distribution.
    (a) Write down the standard deviation of \(W\).
    (b) Find the probability that the total number of calls received in a randomly chosen period of 2 hours is less than 30 .
  2. It is given instead that \(W\) has a uniform distribution on \([ 1 , N ]\). Calculate the value of \(\mathrm { P } ( W > 3 )\).