Question

One of the more contentious issues is whether there should be the death penalty for a person convicted of murder. According to estimates by Gallup, the percentages of U.S. adults that approve of, disapprove of, and have no opinion about the death penalty are 61%, 35%, and 4%, respectively. Suppose that three U.S. adults are randomly selected and asked their position on the death penalty. a. Find the probability that the first two approve and the third disapproves. b. Find the probability that exactly two of the three approve and one disapproves. c. In doing your calculations in parts (a) and (b), are you assuming sampling with replacement or sampling without replacement? Does it make a difference which of those two types of sampling is used? Explain your answers. 

          One of the more contentious issues is whether there should be the death penalty for a person convicted of murder. According to estimates by Gallup, the percentages of U.S. adults that approve of, disapprove of, and have no opinion about the death penalty are 61%, 35%, and 4%, respectively. Suppose that three U.S. adults are randomly selected and asked their position on the death penalty.
a. Find the probability that the first two approve and the third disapproves.
b. Find the probability that exactly two of the three approve and one disapproves.
c. In doing your calculations in parts (a) and (b), are you assuming sampling with replacement or sampling without replacement? Does it make a difference which of those two types of sampling is used? Explain your answers.
Show more…

Added by Vicenta H.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
One of the more contentious issues is whether there should be the death penalty for a person convicted of murder. According to estimates by Gallup, the percentages of U.S. adults that approve of, disapprove of, and have no opinion about the death penalty are 61%, 35%, and 4%, respectively. Suppose that three U.S. adults are randomly selected and asked their position on the death penalty. a. Find the probability that the first two approve and the third disapproves. b. Find the probability that exactly two of the three approve and one disapproves. c. In doing your calculations in parts (a) and (b), are you assuming sampling with replacement or sampling without replacement? Does it make a difference which of those two types of sampling is used? Explain your answers.
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty Jennifer Stoner
David Collins verified

Lucas Finney and 89 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
in-the-survey-on-the-death-penalty-you-read-about-in-the-chapter-the-gallup-poll-actually-split-the-99396

In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” The other 510 were asked “Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?” Seems like the same question, but sometimes the order of the choices matters. Asked the first question, 58% said the death penalty was fairly applied; only 54% said so with the second wording. a) What kind of bias may be present here? b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied? c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

Joanna Q.
in-the-survey-on-the-death-penalty-you-read-about-in-the-chapter-the-gallup-poll-actually-split-the-

In the survey on the death penalty you read about in the chapter, the Gallup Poll actually split the sample at random, asking 510 respondents the question quoted earlier, “Generally speaking, do you believe the death penalty is applied fairly or unfairly in this country today?” The other 510 were asked “Generally speaking, do you believe the death penalty is applied unfairly or fairly in this country today?” Seems like the same question, but sometimes the order of the choices matters. Asked the first question, 58% said the death penalty was fairly applied; only 54% said so with the second wording. a) What kind of bias may be present here? b) If we combine them, considering the overall group to be one larger random sample of 1020 respondents, what is a 95% confidence interval for the proportion of the general public that thinks the death penalty is being fairly applied? c) How does the margin of error based on this pooled sample compare with the margins of error from the separate groups? Why?

STATS Modeling The World

From the Data at Hand to the World at Large

Confidence Intervals for Proportions
in-a-recent-survey-about-capital-punishment-64-of-the-respondents-said-that-they-support-capital-punishment-females-comprised-48-of-the-sample-and-46-of-females-supported-capital-punishment-26814

In a recent survey about capital punishment, 64% of the respondents said that they support capital punishment. Females comprised 48% of the sample, and 46% of females supported capital punishment. Answer the following questions directly in the box below: When answering the questions below, make sure to explain your answers (show how you got the answers). More than half of the points for each question are allocated to your explanations. Question 20 (14 points): a. What is the probability that a randomly selected person is both female and a capital punishment supporter? (4 points) b. Suppose we select a person who does not support capital punishment; what is the probability that the person is male? (4 points) c. If you were to randomly draw 250 females from the population described above: what would be the probability that the sample proportion of females supporting capital punishment is larger than 45 percent? (6 points) Type your answers directly in the box below:

Samriddhi S.
*

Recommended Textbooks

-
Elementary Statistics a Step by Step Approach

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition
achievement 1,460 solutions
The Practice of Statistics for AP

The Practice of Statistics for AP

Daren S. Starnes, Daniel S. Yates, David S. Moore 4th Edition
achievement 1,867 solutions
Introductory Statistics

Introductory Statistics

Barbara Illowsky, Susan Dean 1st Edition
achievement 1,333 solutions
*

Transcript

-
00:01 So for part a here, to find the probability of approve, approve, disapprove, assuming that each individual result is independent, this would be equal to the probability of approval times the probability of approval, times the probability of disapproval.
00:23 So plugging in our values, we have that probability of approve is 0 .61.
00:28 So we have 0 .61 times 0 .61, times probability of disapproval, which is 0 .35.
00:35 So we get a result of roughly 0 .1302.
00:43 Then, for part b, let's see here, the probability that exactly two of the three approve and one disapproves, so probability of if x is equal to the number of people who disapprove, okay, actually, treating this as, i was going to treat this as a binomial, that's not quite appropriate, but saying it's probability of 2a, d, we can think of that as being probability of approve, approve, disapprove, plus probability of approve, disapprove, approve, plus the probability of disapprove, approve, approve...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever