/*! 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 36 The customer service department ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 36

The customer service department of Universal Instruments, manufacturer of the Galaxy home computer, conducted a survey among customers who had returned their purchase registration cards. Purchasers of its deluxe model home computer were asked to report the length of time \((t)\) in days before service was required. a. Describe a sample space corresponding to this survey. b. Describe the event \(E\) that a home computer required service before a period of 90 days had elapsed. c. Describe the event \(F\) that a home computer did not require service before a period of 1 yr had elapsed.

Short Answer

Expert verified
The sample space for this survey is defined as \(S = \{t : t \in \mathbb{N}, 0 \leq t \leq 365 \}\), representing all possible lengths of time \((t)\) in days before service was required within the first year of purchase. Event \(E\) is defined as \(E = \{t \in S : t \leq 90 \}\), representing the home computers that required service within 90 days. Event \(F\) is an empty set (\(F = \emptyset\)), as our sample space only considers days within the first year, and event \(F\) pertains to home computers that did not require service before a period of 1 year had elapsed.

Step by step solution

01

Define the sample space

The sample space corresponds to the set of all possible outcomes of this survey. In this case, the possible outcomes are the number of days \((t)\) before service was required for each Galaxy home computer. We can define the sample space as: \[ S = \{t : t \in \mathbb{N}, 0 \leq t \leq 365 \} \] where \(\mathbb{N}\) denotes the set of natural numbers. Note that we have limited the maximum number of days to 365 because we're interested in the service required within the first year of the purchase.
02

Describe event E

Event \(E\) is the event that a home computer required service before a period of 90 days had elapsed. In terms of our sample space, \(E\) can be described as the set of outcomes where the length of time \((t)\) before service required is less than or equal to 90 days: \[ E = \{t \in S : t \leq 90 \} \]
03

Describe event F

Event \(F\) is the event that a home computer did not require service before a period of 1 year (365 days) had elapsed. In terms of our sample space, \(F\) can be described as the set of outcomes where the length of time \((t)\) before service required is greater than 365 days: \[ F = \{t \in S : t > 365 \} \] However, since we have defined our sample space \(S\) as only containing the days within the first year, the event \(F\) is, in fact, an empty set: \[ F = \emptyset \] This means that according to our sample space, there is no home computer that did not require service before a period of 1 year had elapsed.

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

Suppose the probability that Bill can solve a problem is \(p_{1}\) and the probability that Mike can solve it is \(p_{2}\). Show that the probability that Bill and Mike working independently can solve the problem is \(p_{1}+p_{2}-p_{1} p_{2}\).

Determine whether the given experiment has a sample space with equally likely outcomes. Two fair dice are rolled, and the sum of the numbers appearing uppermost is recorded.

Let \(S=\left\\{s_{1}, s_{2}, s_{3}, s_{4}, s_{5}\right\\}\) be the sample space associated with an experiment having the following probability distribution: $$\begin{array}{llllll} \hline \text { Outcome } & s_{1} & s_{2} & s_{3} & s_{4} & s_{5} \\ \hline \text { Probability } & \frac{1}{14} & \frac{3}{14} & \frac{6}{14} & \frac{2}{14} & \frac{2}{14} \\ \hline \end{array}$$ Find the probability of the event: a. \(A=\left\\{s_{1}, s_{2}, s_{4}\right\\}\) b. \(B=\left\\{s_{1}, s_{5}\right\\}\) c. \(C=S\)

A study of the faculty at U.S. medical schools in 2006 revealed that \(32 \%\) of the faculty were women and \(68 \%\) were men. Of the female faculty, \(31 \%\) were full/ associate professors, \(47 \%\) were assistant professors, and \(22 \%\) were instructors. Of the male faculty, \(51 \%\) were full/associate professors, \(37 \%\) were assistant professors, and \(12 \%\) were instructors. If a faculty member at a U.S. medical school selected at random holds the rank of full/associate professor, what is the probability that she is female?

Two hundred workers were asked: Would a better economy lead you to switch jobs? The results of the survey follow: $$ \begin{array}{lccccc} \hline \text { Answer } & \begin{array}{c} \text { Very } \\ \text { likely } \end{array} & \begin{array}{c} \text { Somewhat } \\ \text { likely } \end{array} & \begin{array}{c} \text { Somewhat } \\ \text { unlikely } \end{array} & \begin{array}{c} \text { Very } \\ \text { unlikely } \end{array} & \begin{array}{c} \text { Don't } \\ \text { know } \end{array} \\ \hline \text { Respondents } & 40 & 28 & 26 & 104 & 2 \\ \hline \end{array} $$ If a worker is chosen at random, what is the probability that he or she a. Is very unlikely to switch jobs? b. Is somewhat likely or very likely to switch jobs?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.