The call centre decides to update its model to allow for the fact that calls arrive less regularly when the phonelines have only just opened. For the first hour, 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 9T
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The call centre decides to update its model to allow for the fact that calls arrive less
regularly when the phonelines have only just opened. For the first hour, 0 ≤ t ≤ 60,
the arrival of calls is now modelled as a time inhomogeneous Poisson process with rate
function
t
for 0 t≤ 30
x(t)
=
2
for 30 <t<60.
Using a normal approximation, calculate a 95% prediction interval for the number
of calls received in the first hour. (It may be helpful to recall that if Z~N(0, 1)
is a standard normal distribution then P(Z < 1.96) = 0.975.)
Transcribed Image Text:The call centre decides to update its model to allow for the fact that calls arrive less regularly when the phonelines have only just opened. For the first hour, 0 ≤ t ≤ 60, the arrival of calls is now modelled as a time inhomogeneous Poisson process with rate function t for 0 t≤ 30 x(t) = 2 for 30 <t<60. Using a normal approximation, calculate a 95% prediction interval for the number of calls received in the first hour. (It may be helpful to recall that if Z~N(0, 1) is a standard normal distribution then P(Z < 1.96) = 0.975.)
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