Explanation Given data: Percentage of bike owners who do not currently own a Sierra Cruiser will purchase on the next time they buy a mountain bike is 37 % . Percentage of bike owners who currently own a Sierra Cruiser will purchase on the next time they buy a mountain bike is 12 % . Calculation: 37 % of the bike owners who do not currently own a Sierra Cruiser will purchase on the next time they buy a mountain bike. Therefore, the probability for the mentioned situation is, P 1 = Next purchase Current purchase = 31 % = 0.31 12 % of the bike owners who currently own a Sierra Cruiser will purchase on the next time they buy a mountain bike. Therefore the probability for the mentioned situation is, P 2 = Next purchase Currentl purchase = 12 % = 0.12 Calculate the probability of the bike owners who do have Sierra Cruiser and will not purchase the next time also. P 1 ' = 1 − P 1 Substitute 0.31 for P 1 in the above equation. P 1 ' = 1 − 0.31 = 0.69 Calculate the probability of the bike owners who currently purchased Sierra Cruiser and will not purchase the next time. P 2 ' = 1 − P 2 Substitute 0.12 for P 2 in the above equation. P 2 ' = 1 − 0.12 = 0.88 Hence, the transition matrix of order 2 × 2 for the above probabilities is, T = [ 0.12 0.88 0.31 0.69 ] Assume equilibrium matrix L = [ x y ] …… ( 1 ) Consider the matrix equation. L T = L Substitute [ x y ] for L and [ 0

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ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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Chapter 11.3, Problem 9E

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A long range prediction of Sierra Cruiser’s ultimate market share, assuming that current trends continue.

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Chapter 11.3, Problem 8E

Chapter 11.3, Problem 10E

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To make: A long range prediction of Sierra Cruiser’s ultimate market share, assuming that current trends continue.

Solution Summary: The author calculates the probability of the bike owners who do not currently own a Sierra Cruiser and will not purchase the next time.