Rowan is a musician. His music is hosted on two separate music streaming services, A and S. The number of times Rowan's music is listened to per day on service A follows a Poisson distribution with mean 105. On service S, it follows a Poisson distribution with mean 250, independently of service A. Let T be the total number of times Rowan's music is listened to per day across both streaming services. a State the distribution of T. b Find the probability that Rowan's music will be listened to more than 400 times in a day.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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2 Rowan is a musician. His music is hosted on two separate music streaming services, A and S.
The number of times Rowan's music is listened to per day on service A follows a Poisson
distribution with mean 105.
On service S, it follows a Poisson distribution with mean 250, independently of service A.
Let T be the total number of times Rowan's music is listened to per day across both streaming
services.
a State the distribution of T.
6 Find the probability that Rowan's music will be listened to more than 400 times in a day.
Transcribed Image Text:2 Rowan is a musician. His music is hosted on two separate music streaming services, A and S. The number of times Rowan's music is listened to per day on service A follows a Poisson distribution with mean 105. On service S, it follows a Poisson distribution with mean 250, independently of service A. Let T be the total number of times Rowan's music is listened to per day across both streaming services. a State the distribution of T. 6 Find the probability that Rowan's music will be listened to more than 400 times in a day.
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