/*! 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 2 Classify each of the following n... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 2

Classify each of the following numerical variables as either discrete or continuous: a. The fuel efficiency (in miles per gallon) of an automobile b. The amount of rainfall at a particular location during the next year c. The distance that a person throws a baseball d. The number of questions asked during a 1 -hr lecture e. The tension (in pounds per square inch) at which a tennis racket is strung f. The amount of water used by a household during a given month g. The number of traffic citations issued by the highway patrol in a particular county on a given day

Short Answer

Expert verified
a. The fuel efficiency of an automobile is a continuous variable.\nb. The amount of rainfall at a particular location during the next year is a continuous variable.\nc. The distance that a person throws a baseball is a continuous variable.\nd. The number of questions asked during a 1 -hr lecture is a discrete variable.\ne. The tension at which a tennis racket is strung is a continuous variable.\nf. The amount of water used by a household during a given month is a continuous variable.\ng. The number of traffic citations issued by the highway patrol in a particular county on a given day is a discrete variable.

Step by step solution

01

Classify Fuel Efficiency

Fuel efficiency (in miles per gallon) of an automobile involves measurements with potentially infinite possibilities. Given the fact that the fuel efficiency can take on any value in a range, it is a continuous variable.
02

Classify Rainfall

Rainfall measured at a specific location during the next year can theoretically take on any value within a certain range depending on the climate conditions. This makes it a continuous variable.
03

Classify Distance

The distance that a person throws a baseball can take on any value, from zero to potentially several hundred feet, depending on the person's strength. This is a continuous variable.
04

Classify Questions Asked

The number of questions asked during a 1 hour lecture can be counted, and thus, this is a discrete variable.
05

Classify Tension

The tension (in pounds per square inch) at which a tennis racket is strung is a measurement that can take any value within the range of possible tensions. Thus, it is a continuous variable.
06

Classify Water Usage

The amount of water used by a household during a given month can theoretically take any value within a certain range. Therefore, it is a continuous variable.
07

Classify Traffic Citations

The number of traffic citations issued by the highway patrol in a particular county on a given day can be counted. Therefore, this is a discrete 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 numerical variables that take on a countable number of distinct values. This means that you can count the values systematically and they cannot have intermediate values.
A good example is the number of questions asked during a lecture. Since you can count the exact number of questions (like 1, 2, 3, etc.), it is a discrete variable. It can't be 2.5 or 3.7 questions鈥攐nly whole numbers make sense.
In practice, discrete variables often describe things like the number of people in a room, the count of books on a shelf, or as seen in the original exercise, the number of traffic citations issued daily. These variables are typically reported using counts or frequencies.
Continuous Variables
Continuous variables are numerical values that can take on an infinite number of points along a continuum. Unlike discrete variables, they can have any value within a limited range. This means they can take on fractional values.
For instance, the fuel efficiency of a vehicle, measured in miles per gallon, is continuous. You might find a car that offers 25.3 mpg or 34.6 mpg. These values are not restricted to whole numbers. Other examples include measurements like distance, time, or temperature. In our original examples, rainfall amount and water usage also fall into this category.
The essence of continuous variables is their endless precision. It's like dividing a pie: theoretically, you can keep cutting it into finer and finer slices without ever needing to stop.
Numerical Data Classification
Numerical data classification is a key part of organizing your statistical data. It helps you understand whether the data you have is better described by discrete or continuous variables, which can affect how you analyze it.
  • Discrete classification helps you when dealing with counts: think of things like event occurrences or number of attempts.
  • Continuous classification applies to measurements where precision is key: think of fuel efficiencies or material measurements.
It's important to classify data correctly because it affects statistical methods used for data analysis. For example, calculating averages of continuous data like rainfall can help in different ways compared to tallying discrete data like citation counts.
Correct classification eases the path to clear insights from your data.

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

Consider the variable \(x=\) time required for a college student to complete a standardized exam. Suppose that for the population of students at a particular university, the distribution of \(x\) is well approximated by a normal curve with mean \(45 \mathrm{~min}\) and standard deviation \(5 \mathrm{~min}\). a. If \(50 \mathrm{~min}\) is allowed for the exam, what proportion of students at this university would be unable to finish in the allotted time? b. How much time should be allowed for the exam if we wanted \(90 \%\) of the students taking the test to be able to finish in the allotted time? c. How much time is required for the fastest \(25 \%\) of all students to complete the exam?

Determine the following standard normal ( \(z\) ) curve areas: a. The area under the \(z\) curve to the left of \(1.75\) b. The area under the \(z\) curve to the left of \(-0.68\) c. The area under the \(z\) curve to the right of \(1.20\) d. The area under the \(z\) curve to the right of \(-2.82\) e. The area under the \(z\) curve between \(-2.22\) and \(0.53\) f. The area under the \(z\) curve between \(-1\) and 1 g. The area under the \(z\) curve between \(-4\) and 4

Accurate labeling of packaged meat is difficult because of weight decrease resulting from moisture loss (defined as a percentage of the package's original net weight). Suppose that the normal distribution with mean value \(4.0 \%\) and standard deviation \(1.0 \%\) is a reasonable model for the variable \(x=\) moisture loss for a package of chicken breasts. (This model is suggested in the paper "Drained Weight Labeling for Meat and Poultry: An Economic Analysis of a Regulatory Proposal," Journal of Consumer Affairs \([1980]: 307-325 .)\) a. What is the probability that \(x\) is between \(3.0 \%\) and \(5.0 \%\) ? b. What is the probability that \(x\) is at most \(4.0 \%\) ? c. What is the probability that \(x\) is at least \(7 \%\) ? d. Describe the largest \(10 \%\) of the moisture loss distribution.

Consider babies bom in the "normal" range of 37-43 weeks gestational age. Extensive data support the assumption that for such babies born in the United States, birth weight is normally distributed with mean \(3432 \mathrm{~g}\) and standard deviation \(482 \mathrm{~g}\) ("Are Babies Normal," The \(-302\) ). (The investigad data from a particular s intervals, the hisbut after further investi1 that this was due ht in grams and others measuring to the nearest ounce and then converting to grams. A modified choice of class intervals that allowed for this measurement difference gave a histogram that was well described by a normal distribution.) a. What is the probability that the birth weight of a randomly selected baby of this type exceeds \(4000 \mathrm{~g}\) ? is between 3000 and \(4000 \mathrm{~g}\) ? b. What is the probability that the birth weight of a randomly selected baby of this type is either less than \(2000 \mathrm{~g}\) or greater than \(5000 \mathrm{~g}\) ? c. What is the probability that the birth weight of a randomly selected baby of this type exceeds \(7 \mathrm{lb}\) ? (Hint: \(1 \mathrm{lb}=453.59 \mathrm{~g} .\) ) d. How would you characterize the most extreme \(0.1 \%\) of all birth weights?

Determine the value of \(z^{*}\) such that a. \(z^{*}\) and \(-z^{*}\) separate the middle \(95 \%\) of all \(z\) values from the most extreme \(5 \%\) b. \(z^{*}\) and \(-z^{*}\) separate the middle \(90 \%\) of all \(z\) values from the most extreme \(10 \%\) c. \(z^{*}\) and \(-z^{*}\) separate the middle \(98 \%\) of all \(z\) values from the most extreme \(2 \%\) d. \(z^{*}\) and \(-z^{*}\) separate the middle \(92 \%\) of all \(z\) values from the most extreme \(8 \%\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.