/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 98 From experience, a shipping comp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 98

From experience, a shipping company knows that the cost of delivering a small package within 24 hours is \(\$ 14.80 .\) The company charges \(\$ 15.50\) for shipment but guarantees to refund the charge if delivery is not made within 24 hours. If the company fails to deliver only \(2 \%\) of its packages within the 24 -hour period, what is the expected gain per package?

Short Answer

Expert verified
Answer: The expected gain per package is $0.39.

Step by step solution

01

Identify the possible outcomes and their probabilities

There are two possible outcomes for each package delivery: 1. The package is delivered within 24 hours (with a probability of 98% or 0.98). In this case, the company keeps the shipment charge (\(15.50) and pays the cost of delivery (\)14.80). 2. The package is not delivered within 24 hours (with a probability of 2% or 0.02). In this case, the company refunds the shipment charge and still pays the cost of delivery.
02

Calculate the gain for each outcome

To calculate the gain for each outcome, we need to subtract the cost of delivery from the fee for each scenario. 1. Delivered within 24 hours: Gain = Fee - Cost = \(15.50 - 14.80 = \)0.70 2. Not delivered within 24 hours: Gain = Fee - Cost = \(0 - 14.80 = \)-14.80
03

Calculate the expected value

Now, we can compute the expected value by multiplying each outcome's gain by its probability and summing up the results: Expected Gain = (Gain1)*(Probability1) + (Gain2)*(Probability2) Expected Gain = (\(0.70)*(0.98) + (-\)14.80)*(0.02) Expected Gain = \(0.686 - \)0.296 = $0.39 The expected gain per package is \(\$ 0.39\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Your family vacation involves a cross-country air flight, a rental car, and a hotel stay in Boston. If you can choose from four major air carriers, five car rental agencies, and three major hotel chains, how many options are available for your vacation accommodations?

To reduce the cost of detecting a disease, blood tests are conducted on a pooled sample of blood collected from a group of \(n\) people. If no indication of the disease is present in the pooled blood sample (as is usually the case), none have the disease. If analysis of the pooled blood sample indicates that the disease is present, each individual must submit to a blood test. The individual tests are conducted in sequence. If, among a group of five people, one person has the disease, what is the probability that six blood tests (including the pooled test) are required to detect the single diseased person? If two people have the disease, what is the probability that six tests are required to locate both diseased people?

Five cards are selected from a 52 -card deck for a poker hand. a. How many simple events are in the sample space? b. A royal flush is a hand that contains the \(\mathrm{A}, \mathrm{K}, \mathrm{Q}, \mathrm{J},\) and \(10,\) all in the same suit. How many ways are there to get a royal flush? c. What is the probability of being dealt a royal flush?

In how many ways can you select two people from a group of 20 if the order of selection is not important?

Experience has shown that, \(50 \%\) of the time, a particular unionmanagement contract negotiation led to a contract settlement within a 2 -week period, \(60 \%\) of the time the union strike fund was adequate to support a strike, and \(30 \%\) of the time both conditions were satisfied. What is the probability of a contract settlement given that the union strike fund is adequate to support a strike? Is settlement of a contract within a 2 -week period dependent on whether the union strike fund is adequate to support a strike?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.