Explanation Given info: A warehouse club offers 2 types of memberships- regular membership, R for a low annual fee and upgraded membership, U for a higher annual fee and having additional benefits such as extended shopping hours, additional discounts, cashbacks, etc. The warehouse has 20% of its members with upgraded membership. They wish to increase the number of upgraded members and stations sales associates at the entrance of the store to explain the benefits of an upgraded membership. At a certain time point, 5 customers enter the store. As each of the customers has either an upgraded membership ( U ) or a regular membership ( R ), there are 2 5 = 32 combinations of memberships that are possible, among the 5 customers. The membership types of the customers are independent of each other. Calculation: It is given that the probability that a customer has an upgraded membership is: P ( U ) = 0.2 and the probability that a customer has a regular membership is: P ( R ) = 0.8 . Moreover, the membership types of the customers are independent of each other. Thus, P ( R R R R R ) = P ( R ) P ( R ) P ( R ) P ( R ) P ( R ) = ( 0.8 ) 5 = 0.32768. P ( U R R R R ) = P ( U ) P ( R ) P ( R ) P ( R ) P ( R ) = ( 0.2 ) ( 0.8 ) 4 = 0.08192. As probability does not depend upon the order of multiplying U and R , thus, P ( U R R R R ) = P ( R U R R R ) = P ( R R U R R ) = P ( R R R U R ) = P ( R R R R U ) . Thus, P ( U R R R R ) = P ( R U R R R ) = P ( R R U R R ) = P ( R R R U R ) = P ( R R R R U ) = 0.08192. P ( U U R R R ) = P ( U ) P ( U ) P ( R ) P ( R ) P ( R ) = ( 0.2 ) 2 ( 0.8 ) 3 = 0.02048. As probability does not depend upon the order of multiplying U and R , P ( U U R R R ) = P ( U R U R R ) = P ( U R R U R ) = P ( U R R R U ) = P ( R U U R R ) = P ( R U R U R ) = P ( R U R R U ) = P ( R R U U R ) = P ( R R U R U ) = P ( R R R U U ) = 0

Statistics for Business and Economics (13th Edition)

13th Edition

ISBN: 9780134506593

Author: James T. McClave, P. George Benson, Terry Sincich

Publisher: PEARSON

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Chapter 4, Problem 4.1.4A

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To find: The probability of each of the 32 outcomes.

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Chapter 4 Solutions

Statistics for Business and Economics (13th Edition)

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The probability of each of the 32 outcomes.

Solution Summary: The author explains that a warehouse club offers two types of memberships: regular membership, low annual fee, and upgraded membership.

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To find: The probability of each of the 32 outcomes.

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Chapter 4 Solutions