SPS SPS FM Statistics 2023 January — Question 1

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2023
SessionJanuary
TopicPoisson Distribution
TypeScaled time period probability

1. Indre works on reception in an office and deals with all the telephone calls that arrive. Calls arrive randomly and, in a 4-hour morning shift, there are on average 80 calls.
  1. Using a suitable model, find the probability of more than 4 calls arriving in a particular 20-minute period one morning. Indre is allowed 20 minutes of break time during each 4 -hour morning shift, which she can take in 5-minute periods. When she takes a break, a machine records details of any call in the office that Indre has missed. One morning Indre took her break time in 4 periods of 5 minutes each.
  2. Find the probability that in exactly 3 of these periods there were no calls.