Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q49E (page 239)

The next presidential election. A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters are randomly selected from the population of all eligible voters.

a. Analyze the potential outcomes for the sample using the binomial random variable.

b. Use a binomial probability table to find the probability that more than 12 of the eligible voters sampled will vote in the next presidential election.

c. Use a binomial probability table to find the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election.

Short Answer

Expert verified
  1. A binomial random variable can have any number between 0 as well as n.
  2. PX⩾12=0.772
  3. P16⩽X⩽20=0.714

Step by step solution

01

Given information

70% of all eligible voters will vote in the next presidential election

n=20

02

(a)Finding potential outcomes

The experiment comprises of n similar as well as independent trials, with n predetermined. Every trial can have one of two results: success (S) as well as failures (F), with the likelihood of succeeding (p) being equal from trial to trial. A binomial random variable can have any number between 0 as well as n.

03

(b) Finding the probability that more than 12 of the eligible voters sampled will vote in the next presidential election

PX⩾12=PX=12+PX=13+...+PX=20=∑i=122020ipi1-p20-i=0.772

Thus, the required probability is 0.772.

04

(c) Finding the probability that more than 10 but fewer than 16 of the 20 eligible voters sampled will vote in the next presidential election

P16⩽X⩽20=PX=16+PX=17+...+PX=20=∑i=162020ipi1-p20-i=0.714

Thus, the required probability is 0.714.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Suppose x is a binomial random variable with n = 3 and p = .3.

  1. Calculate the value of p(x),role="math" localid="1653657859012" x=0,1,2,3,using the formula for a binomial probability distribution.
  2. Using your answers to part a, give the probability distribution for x in tabular form.

4.112 California’s electoral college votes. During a presidential election, each state is allotted a different number of votes in the Electoral College, depending on the population. For example, California is allotted 55 votes (the most) while several states (including the District of Columbia) are allotted 3 votes each (the least). When a presidential candidate wins the popular vote in a state, the candidate wins all the Electoral College votes in that state. To become president, a candidate must win 270 of the total of 538 votes in the Electoral College. Chance(Winter 2010) demonstrated the impact on the presidential election of winning California. Assuming a candidate wins California’s 55 votes, the number of additional Electoral College votes the candidate will win can be approximated by a normal distribution with μ=241.5votes and σ=49.8votes. If a presidential candidate wins the popular vote in California, what are the chances that he or she becomes the next U.S. president?

Ranking PhD programs in economics. Refer to the SouthernEconomic Journal(April 2008) rankings of PhD programsin economics at 129 colleges and universities, Exercise 2.103(p. 117). Recall that the number of publications published byfaculty teaching in the PhD program and the quality of thepublications were used to calculate an overall productivityscore for each program. The mean and standard deviationof these 129 productivity scores were then used to computea z-score for each economics program. The data (z-scores)for all 129 economic programs are saved in the accompanying

file. A Minitab normal probability plot for the z-scores isshown below. Use the graph to assess whether the data areapproximately normal.

The binomial probability distribution is a family of probability distributions with every single distribution depending on the values of n and p. Assume that x is a binomial random variable with n = 4.

  1. Determine a value of p such that the probability distribution of x is symmetric.
  2. Determine a value of p such that the probability distribution of x is skewed to the right.
  3. Determine a value of p such that the probability distribution of x is skewed to the left.
  4. Graph each of the binomial distributions you obtained in parts a, b, and c. Locate the mean for each distribution on its graph.\
  5. In general, for what values of p will a binomial distribution be symmetric? Skewed to the right? Skewed to the left?

Privacy and information sharing. Refer to the Pew Internet & American Life Project Survey (January 2016), Exercise 4.48 (p. 239). The survey revealed that half of all U.S. adults would agree to participate in a free cost-saving loyalty card program at a grocery store, even if the store could potentially sell these data on the customer’s shopping habits to third parties. In a random sample of 250 U.S. adults, let x be the number who would participate in the free loyalty card program.

a. Find the mean of x. (This value should agree with your answer to Exercise 4.48c.)

b. Find the standard deviation of x.

c. Find the z-score for the value x = 200.

d. Find the approximate probability that the number of the 250 adults who would participate in the free loyalty card program is less than or equal to 200.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.

Sign-up for free