Calculator Allowed: Yes



Transcription of this question: Willow finds that she receives approximately 70 emails per working day.She decides to model the number of emails received per working day using the randomvariable X, where X follows a Poisson distribution with mean 70.(a) Using this distribution model, find(ii) the standard deviation of X.In order to test her model, Willow records the number of emails she receives perworking day over a period of 6 months. The results are shown in the following table.Number of emails received (x) Number of days40 X 4950SXS5960 S x S 6970 7980 8990 S x S 99100 sxS109110 SXS119From the table, calculate215405336(ii)an estimate for the mean number of emails received per working day;an estimate for the standard deviation of the number of emails received perworking day.[5](c) Give one piece of evidence that suggests Willow’s Poisson distribution model is not agood fit.Archie works for a different company and knows that he receives emails according to aPoisson distribution, with a mean of emails per day.(d)Suppose that the probability of Archie receiving more than 10 emails in total on any oneday is 0.99. Find the value of A.Now suppose that Archie received exactly 20 emails in total in a consecutive two dayperiod. Show that the probability that he received exactly 10 of them on the first day isindependent of .[5]

Leave a Reply