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The management at a fast-food outlet is interested in the

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 15E Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 15E

The management at a fast-food outlet is interested in the joint behavior of the random variables Y1, defined as the total time between a customer’s arrival at the store and departure from the service window, and Y2, the time a customer waits in line before reaching the service window. Because Y1 includes the time a customer waits in line, we must have Y1 ≥ Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modeled by the probability density function

with time measured in minutes. Find

a P ( Y 1 < 2, Y2 > 1).

b P ( Y 1 ≥ 2Y2).

c P ( Y 1 − Y2 ≥ 1). (Notice that Y1 − Y2 denotes the time spent at the service window.)

Step-by-Step Solution:

Solution:

Step 1 of 2:

Let Y1 be the total time between a customer's arrival at the store and departure from the service window.

And Y2 be the time a customer waits in line before reaching the service window.

 

The joint density function of Y1 and Y2 is given by,

                         

We have to find

  1. P(Y1<2, Y2>1).
  2. P(Y1
  3. P(Y1


Step 2 of 2

Chapter 5, Problem 15E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Since the solution to 15E from 5 chapter was answered, more than 334 students have viewed the full step-by-step answer. The answer to “The management at a fast-food outlet is interested in the joint behavior of the random variables Y1, defined as the total time between a customer’s arrival at the store and departure from the service window, and Y2, the time a customer waits in line before reaching the service window. Because Y1 includes the time a customer waits in line, we must have Y1 ? Y2. The relative frequency distribution of observed values of Y1 and Y2 can be modeled by the probability density function with time measured in minutes. Finda P ( Y 1 < 2, Y2 > 1).b P ( Y 1 ? 2Y2).c P ( Y 1 ? Y2 ? 1). (Notice that Y1 ? Y2 denotes the time spent at the service window.)” is broken down into a number of easy to follow steps, and 126 words. This full solution covers the following key subjects: window, customer, service, waits, line. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The full step-by-step solution to problem: 15E from chapter: 5 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM.

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