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At a certain gas station, 40% of the customers use regular

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 59E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 59E

At a certain gas station, 40% of the customers use regular gas (?A?1), 35% use plus gas (?A?2), and 25% use premium (?A?3). Of those customers using regular gas, only 30% fill their tanks (event ?B?). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. ?What is the probability that the next customer will request plus gas and fill the tank (A2?B)? b.? hat is the probability that the next customer fills the tank? c. ?If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?

Step-by-Step Solution:

Answer : Step 1 : Given,at a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A 3). P(A )1= 40 = 0.40 100 P(A )2= 35 = 0.35 100 P(A ) = 25 = 0.25 3 100 Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. Then, P( B ) = 30 = 0.3 A1 100 B 60 P( A ) = 100 = 0.4 2 P( B ) = 50 = 0.5 A3 100 Therefore, B P(A 1B) = P(A 1 P( )A1 P(A 1B) = (0.40) (0.3) P(A B) = 0.12 1 B P(A 2B) = P(A 2 P( )A2 P(A B) 2 = (0.35) (0.60) P(A 2B)= 0.21 P(A B) = P(A ) P( )B 3 3 A3 P(A B)= (0.25) (0.50) 3 P(A 3B) = 0.125 a). Let the probability that the next customer will request plus gas and fill the tank. 2 Here A2B = 0.14

Step 2 of 3

Chapter 2, Problem 59E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 59E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Since the solution to 59E from 2 chapter was answered, more than 623 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. This full solution covers the following key subjects: gas, plus, fill, those, use. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “At a certain gas station, 40% of the customers use regular gas (?A?1), 35% use plus gas (?A?2), and 25% use premium (?A?3). Of those customers using regular gas, only 30% fill their tanks (event ?B?). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. a. ?What is the probability that the next customer will request plus gas and fill the tank (A2?B)? b.? hat is the probability that the next customer fills the tank? c. ?If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?” is broken down into a number of easy to follow steps, and 103 words.

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