Question

16 pointsl The National Broadband Network (NBN) is an Australian national wholesale-only, open access data network. The NBN project started in 2011 and the Fibre to the Premises (FTTP) rollout is planned to reach approximately 93% of premises in Australia by June 2021 . In November 2016, the rollout in The Ponds, a northwest suburb of Sydney was completed. In December 2016, A telco Company, Exetel Pty Ltd, was promoting an NBN connection to their existing ADSL customers in the area. The number of NBN connection online applications received by Exetel on a particular day (24 hours, counting from the mid-night 00:00 to the next midnight) is assumed to follow a Poisson distribution with mean 16. (i) [4 points] Find the probability that at least 10 applications are received on a day. Verify your answer using MS Excel. (ii) [4 points! Find the probability that more than 80 applications are received on 5 days using MS Excel. You do not need to calculate the individual probabilities manually. (iii) [4 points] Find the probability that Exetel does not receive any application in the two hours between 00.00 and 02:00am on a particular night. What additional assumption is required to get this answer?

Answer 1

(i) Here the poission parameter $\lambda$ = 16

so if x is the number of application received on a given day

Pr(x>= 10) = 1 - POISSONCDF (x < = 9 ; 16) = 1 - 0.0433 = 0.9567

(ii) here expected number of application to be received in 5 days = 5 * 16 = 80

so

Pr(x > 80) = 1- POISSONCDF (x < = 80 ; 80) = 1 - 0.5297 = 0.4703

(iii) expected number ofapplication tobe received in the 2 hours from 00.00 and 02.00 am = (16/24)* 2 = 4/3

Here assumption is "the number of applications received are independent of the time they are coming"

so

Pr(x = 0 ; 4/3)= e^-4/3 = 0.2636