/*! 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 1 State whether each of the follow... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 1

State whether each of the following random variables is discrete or continuous: a. The number of defective tires on a car b. The body temperature of a hospital patient c. The number of pages in a book d. The number of draws (with replacement) from a deck of cards until a heart is selected e. The lifetime of a lightbulb

Short Answer

Expert verified
a. Discrete; b. Continuous; c. Discrete; d. Discrete; e. Continuous.

Step by step solution

01

Distinguish Between Discrete and Continuous Variables

This involves identifying whether the random variable under consideration can take on any value within a given interval (continuous) or can only take on distinct, separate values (discrete).
02

Apply Identification to Each Variable

Identify each variable as either discrete or continuous based on the parameter it measures: a. The number of defective tires on a car - This is a discrete variable because the number of defective tires can only be an integer. b. The body temperature of a hospital patient - This is a continuous variable because body temperature can take any value in a certain range. c. The number of pages in a book - This is a discrete variable because the number of pages in a book must be a whole number. d. The number of draws (with replacement) from a deck of cards until a heart is selected - This is a discrete variable because the number of draws is countable. e. The lifetime of a lightbulb - This is a continuous variable because the life of a product can take any value in a certain range.

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

The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (Water Research [1984]: \(1169-1174\) ) suggests the uniform distribution on the interval from \(7.5\) to 20 as a model for \(x=\) depth (in centimeters) of the bioturbation layer in sediment for a certain region. a. Draw the density curve for \(x\). b. What is the height of the density curve? c. What is the probability that \(x\) is at most 12 ? d. What is the probability that \(x\) is between 10 and 15 ? Between 12 and 17 ? Why are these two probabilities equal?

The article "FBI Says Fewer than 25 Failed Polygraph Test" (San Luis Obispo Tribune, July 29,2001 ) states that false-positives in polygraph tests (i.e., tests in which an individual fails even though he or she is telling the truth) are relatively common and occur about \(15 \%\) of the time. Suppose that such a test is given to 10 trustworthy individuals. a. What is the probability that all 10 pass? b. What is the probability that more than two fail, even though all are trustworthy? c. The article indicated that 500 FBI agents were required to take a polygraph test. Consider the random variable \(x=\) number of the 500 tested who fail. If all 500 agents tested are trustworthy, what are the mean and standard deviation of \(x ?\) d. The headline indicates that fewer than 25 of the 500 agents tested failed the test. Is this a surprising result if all 500 are trustworthy? Answer based on the values of the mean and standard deviation from Part (c).

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the variable \(x=\) actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean \(15.0\) gallons and standard deviation \(0.1\) gallon. a. What is the probability that a randomly selected tank will hold at most \(14.8\) gallons? b. What is the probability that a randomly selected tank will hold between \(14.7\) and \(15.1\) gallons? c. If two such tanks are independently selected, what is the probability that both hold at most 15 gallons?

Flashlight bulbs manufactured by a certain company are sometimes defective. a. If \(5 \%\) of all such bulbs are defective, could the techniques of this section be used to approximate the probability that at least five of the bulbs in a random sample of size 50 are defective? If so, calculate this probability; if not, explain why not. b. Reconsider the question posed in Part (a) for the probability that at least 20 bulbs in a random sample of size 500 are defective.

The paper "Risk Behavior, Decision Making, and Music Genre in Adolescent Males" (Marshall University, May 2009 ) examined the effect of type of music playing and performance on a risky, decision-making task. a. Participants in the study responded to a questionnaire that was used to assign a risk behavior score. Risk behavior scores (read from a graph that appeared in the paper) for 15 participants follow. Use these data to construct a normal probability plot (the normal scores for a sample of size 15 appear in the previous exercise). \(\begin{array}{llllllll}102 & 105 & 113 & 120 & 125 & 127 & 134 & 135\end{array}\) \(\begin{array}{lllllll}139 & 141 & 144 & 145 & 149 & 150 & 160\end{array}\) b. Participants also completed a positive and negative affect scale (PANAS) designed to measure emotional response to music. PANAS values (read from a graph that appeared in the paper) for 15 participants follow. Use these data to construct a normal probability plot (the normal scores for a sample of size 15 appear in the previous exercise). \(\begin{array}{llllllll}36 & 40 & 45 & 47 & 48 & 49 & 50 & 52\end{array}\) \(\begin{array}{lllllll}53 & 54 & 56 & 59 & 61 & 62 & 70\end{array}\) c. The author of the paper states that he believes that it is reasonable to consider both risk behavior scores and PANAS scores to be approximately normally distributed. Do the normal probability plots from Parts (a) and (b) support this conclusion? Explain.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

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.