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A group of people use an app to track their work outs in the gym everyday. The workouts can be categorized as Strenuous, Moderate, or Light. When the data from the app was reviewed, the following observation was made: Of the people who work out strenuously on a particular day, 40% will work out strenuously the next day and 60% will work out moderately. Of the people who work out moderately on a particular day, 50% will work out strenuously the next day and 50% will work out lightly. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% will work out moderately, and 50% lightly. (a) Set up the 3 x 3 transition matrix with rows and columns labelled S , M, and L. (b) Suppose that on a particular Monday, 80% work out strenuously, 10% moderately, and 10% lightly. What will the distribution be on Wednesday? (You can use a calculator for the matrix multiplication.) (c) Find the stable distribution algebraically.

A group of people use an app to track their work outs in the gym everyday. The workouts can be categorized as Strenuous, Moderate, or Light. When the data from the app was reviewed, the following observation was made: Of the people who work out strenuously on a particular day, 40% will work out strenuously the next day and 60% will work out moderately. Of the people who work out moderately on a particular day, 50% will work out strenuously the next day and 50% will work out lightly. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% will work out moderately, and 50% lightly. (a) Set up the 3 x 3 transition matrix with rows and columns labelled S , M, and L. (b) Suppose that on a particular Monday, 80% work out strenuously, 10% moderately, and 10% lightly. What will the distribution be on Wednesday? (You can use a calculator for the matrix multiplication.) (c) Find the stable distribution algebraically.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 13PT
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A group of people use an app to track their work outs in the gym everyday. The workouts can be categorized as Strenuous, Moderate, or Light. When the data from the app was reviewed, the following observation was made: Of the people who work out strenuously on a particular day, 40% will work out strenuously the next day and 60% will work out moderately. Of the people who work out moderately on a particular day, 50% will work out strenuously the next day and 50% will work out lightly. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% will work out moderately, and 50% lightly. (a) Set up the 3 x 3 transition matrix with rows and columns labelled S , M, and L. (b) Suppose that on a particular Monday, 80% work out strenuously, 10% moderately, and 10% lightly. What will the distribution be on Wednesday? (You can use a calculator for the matrix multiplication.) (c) Find the stable distribution algebraically.
Transcribed Image Text:A group of people use an app to track their work outs in the gym everyday. The workouts can be categorized as Strenuous, Moderate, or Light. When the data from the app was reviewed, the following observation was made: Of the people who work out strenuously on a particular day, 40% will work out strenuously the next day and 60% will work out moderately. Of the people who work out moderately on a particular day, 50% will work out strenuously the next day and 50% will work out lightly. Of the people working out lightly on a particular day, 30% will work out strenuously on the next day, 20% will work out moderately, and 50% lightly. (a) Set up the 3 x 3 transition matrix with rows and columns labelled S , M, and L. (b) Suppose that on a particular Monday, 80% work out strenuously, 10% moderately, and 10% lightly. What will the distribution be on Wednesday? (You can use a calculator for the matrix multiplication.) (c) Find the stable distribution algebraically.
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