/*! 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 80 Identify the following as discre... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 80

Identify the following as discrete or continuous random variables: a. Total number of points scored in a football game b. Shelf life of a particular drug c. Height of the ocean's tide at a given location d. Length of a 2-year-old black bass e. Number of aircraft near-collisions in a year

Short Answer

Expert verified
**Question:** Classify each of the following random variables as discrete or continuous: a. Total number of points scored in a football game b. Shelf life of a particular drug c. Height of the ocean's tide at a given location d. Length of a 2-year-old black bass e. Number of aircraft near-collisions in a year **Answer:** a. Discrete b. Continuous c. Continuous d. Continuous e. Discrete

Step by step solution

01

a. Total number of points scored in a football game

The number of points scored in a football game is countable as it consists of a series of specific, distinct values (integers). Therefore, this random variable is discrete.
02

b. Shelf life of a particular drug

The shelf life of a drug is a measurement of time, which can be expressed as a decimal value. Hence, it can take on any value within a specified range (e.g., between 0 and 10 years). This makes it a continuous random variable.
03

c. Height of the ocean's tide at a given location

The height of the ocean's tide is a measurement of length, which can be expressed as a decimal value. Like the shelf life of a drug, it can take on any value within a specified range (e.g., between 0 and 50 feet). Therefore, this random variable is continuous.
04

d. Length of a 2-year-old black bass

The length of a 2-year-old black bass is also a measurement that can be expressed as a decimal value. It can take on any value within a specified range (e.g., between 5 and 30 inches). This makes it a continuous random variable.
05

e. Number of aircraft near-collisions in a year

The number of near-collisions is countable, as it consists of a series of specific, distinct values (integers). Therefore, this random variable is discrete.

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 can take on a finite or countable number of distinct values. These values are often whole numbers due to their nature of being countable. For instance, in a football game, counting the total number of points scored gives you discrete values like 0, 1, 2, 3, and so on. Such variables are measurable using integers. Characteristics of discrete variables include:
  • Distinct and separate values
  • Often represented by whole numbers
  • Can be counted but not measured precisely as fractions or decimals
In practical situations, you might encounter discrete variables in various forms:
  • Number of students in a classroom
  • Number of books on a shelf
  • Number of cars in a parking lot
By understanding the nature of discrete variables, you can easily identify and work with them in different statistical contexts.
Continuous Variables
Continuous variables, on the other hand, represent data that can take on any value within a given range. Because these variables can have an infinite number of potential values, they can be represented with decimals, allowing for very detailed and precise measurements. An example of this concept can be seen in the shelf life of a drug or the height of the ocean's tide. Both are examples of continuous random variables because they can assume any value:
  • A drug's shelf life could be measured precisely down to days or even hours.
  • The ocean's tide height could be measured to millimeters according to fluctuations.
Characteristics of continuous variables include:
  • An infinite range of possible values
  • Can be measured precisely and expressed in decimals or fractions
  • Sensitive to the level of measurement precision
These variables are common in fields requiring high precision, such as pharmaceuticals and environmental science, where detailed precision is crucial.
Probability Concepts
Probability concepts in statistics revolve around understanding how likely an event is to occur. In the context of random variables, probability helps us predict outcomes based on quantitative patterns. There are two primary types of probability distributions:
  • **Discrete probability distribution**: Used with discrete variables, where outcomes are countable and finite. Examples include the roll of a die or the number of students who pass a test.
  • **Continuous probability distribution**: Used with continuous variables where any value within a range is possible. Examples include the probability of someone's exact height or the precise amount of rain in a day.
Each type has its insights and applications:
  • Discrete distributions can be calculated using tools like probability mass functions.
  • Continuous distributions are described with probability density functions.
By grasping these fundamental probability concepts, you can better analyze and predict patterns and outcomes in data involving discrete and continuous random variables.

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 heavy-equipment salesman can contact either one or two customers per day with probabilities \(1 / 3\) and \(2 / 3,\) respectively. Each contact will result in either no sale or a \(\$ 50,000\) sale with probabilities \(9 / 10\) and \(1 / 10,\) respectively. What is the expected value of his daily sales?

A quality-control plan calls for accepting a large lot of crankshaft bearings if a sample of seven is drawn and none are defective. What is the probability of accepting the lot if none in the lot are defective? If \(1 / 10\) are defective? If \(1 / 2\) are defective?

Refer to the experiment conducted by Gregor Mendel in Exercise 4.64 Suppose you are interested in following two independent traits in snap peas-seed texture \((\mathrm{S}=\) smooth, \(\mathrm{s}=\) wrinkled ) and seed color \((\mathrm{Y}=\) yellow, \(\mathrm{y}=\) green \()-\) in a second-generation cross of heterozygous parents. Remember that the capital letter represents the dominant trait. Complete the table with the gene pairs for both traits. All possible pairings are equally likely. a. What proportion of the offspring from this cross will have smooth yellow peas? b. What proportion of the offspring will have smooth green peas? c. What proportion of the offspring will have wrinkled yellow peas? d. What proportion of the offspring will have wrinkled green peas? e. Given that an offspring has smooth yellow peas, what is the probability that this offspring carries one s allele? One s allele and one \(y\) allele?

During the inaugural season of Major League Soccer in the United States, the medical teams documented 256 injuries that caused a loss of participation time to the player. The results of this investigation, reported in The American Journal of Sports Medicine, is shown in the table. \({ }^{3}\) If one individual is drawn at random from this group of 256 soccer players, find the following probabilities: a. \(P(A)\) b. \(P(G)\) c. \(P(A \cap G)\) d. \(P(G \mid A)\) e. \(P(G \mid B)\) f. \(P(G \mid C)\) g. \(P(C \mid P)\) h. \(P\left(B^{c}\right)\)

An experiment is run as follows- the colors red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colors and is asked to choose the one he feels was flashed for the longest time. The experiment is repeated three times with the same subject. a. If all the colors were flashed for the same length of time, find the probability distribution for \(x\), the number of times that the subject chose the color red. Assume that his three choices are independent. b. Construct the probability histogram for the random variable \(x\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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.