/*! 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 183 Decide whether a discrete or con... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 183

Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The number of cracks exceeding one-half inch in 10 miles of an interstate highway. (b) The weight of an injection-molded plastic part. (c) The number of molecules in a sample of gas. (d) The concentration of output from a reactor. (e) The current in an electronic circuit.

Short Answer

Expert verified
(a) Discrete, (b) Continuous, (c) Discrete, (d) Continuous, (e) Continuous.

Step by step solution

01

Understand Discrete and Continuous Variables

A discrete random variable has distinct, separate values, usually counts of items or events. A continuous random variable can take any value within a given range, and often involves measurements.
02

Analyze Variable (a)

Variable (a) is 'the number of cracks exceeding one-half inch in 10 miles of an interstate highway'. Since this is a count of a distinct number of cracks, it is a discrete variable.
03

Analyze Variable (b)

Variable (b) is 'the weight of an injection-molded plastic part'. Weight is a measurement that can take any value within a range and includes decimals, hence it is a continuous variable.
04

Analyze Variable (c)

Variable (c) is 'the number of molecules in a sample of gas'. As it represents countable entities, even if very large, it is a discrete variable.
05

Analyze Variable (d)

Variable (d) is 'the concentration of output from a reactor'. Concentration is a measurement that can take any real number within a specified range, making it a continuous variable.
06

Analyze Variable (e)

Variable (e) is 'the current in an electronic circuit'. Current is a measurable value that can vary continuously, making it a continuous variable.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Discrete Variables
Discrete variables are those that have separate, distinct values. Imagine counting something tangible like the cracks on a highway. Cracks can only form whole numbers, such as 0, 1, 2, etc. These are not fractional. Such counts are inherently finite and distinguish individual occurrences.
Examples include:
  • The number of students in a classroom
  • Number of cars parked in a garage
  • Dice rolls outcome
Discrete variables are an essential part of probability models, especially when dealing with populations that involve counting items or events.
Continuous Variables
Continuous variables are measurements that can take any value within a range. Think of things you can measure, like the weight of a plastic part or the current flowing in a circuit.
In these cases, there aren't just whole numbers but a wide spectrum of possibilities, such as 1.25 pounds or 0.304 amps. Continuous variables are not countable in the discrete sense but can be any infinitesimally small point along a continuum.
Some fields where continuous variables are important include physics, chemistry, and engineering, where precise measurements are crucial for calculations.
Probability Models
Probability models are mathematical representations that depict real-world situations. They help us make sense of how random variables behave.
There are different models based on whether you have discrete or continuous variables. Discrete models, like the binomial or Poisson distributions, deal with countable outcomes. Continuous models, such as the normal distribution, handle uncountable results through calculus-based approaches.
Understanding what type of variable you are working with is critical to selecting the appropriate probability model, thus providing accurate predictions and insights.
Variable Analysis
Variable analysis is the process of determining the nature of a variable. Determining whether a variable is discrete or continuous can impact the statistical methods used.
For instance, analyzing a discrete variable like the number of molecules or highway cracks requires different tools than a continuous variable like weight or current. Analytic techniques focus on the variability, distribution, and behavior of these variables.
This knowledge facilitates constructing accurate models, helping scientists and statisticians to interpret data effectively and make informed decisions.

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

A message can follow different paths through servers on a network. The sender's message can go to one of five servers for the first step; each of them can send to five servers at the second step; each of those can send to four servers at the third step; and then the message goes to the recipient's server. (a) How many paths are possible? (b) If all paths are equally likely, what is the probability that a message passes through the first of four servers at the third step?

It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that now has a total of 75 copies of the program. A sample of copies will be selected from the lot without replacement. (a) If three copies of the software are inspected, determine the probability that exactly one of the defective copies will be found. (b) If three copies of the software are inspected, determine the probability that both defective copies will be found. (c) If 73 copies are inspected, determine the probability that both copies will be found. (Hint: Work with the copies that remain in the lot.)

A reactor's rise time is measured in minutes (and fractions of minutes). Let the sample space for the rise time of each batch be positive, real numbers. Consider the rise times of two batches. Let \(A\) denote the event that the rise time of batch 1 is less than 72.5 minutes, and let \(B\) denote the event that the rise time of batch 2 is greater than 52.5 minutes. Describe the sample space for the rise time of two batches graphically and show each of the following events on a twodimensional plot: (a) \(A\) (b) \(B^{\prime}\) (c) \(A \cap B\) (d) \(A \cup B\)

The probability that a customer's order is not shipped on time is \(0.05 .\) A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events. (a) What is the probability that all are shipped on time? (b) What is the probability that exactly one is not shipped on time? (c) What is the probability that two or more orders are not shipped on time?

A wireless garage door opener has a code determined by the up or down setting of 12 switches. How many outcomes are in the sample space of possible codes?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

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.