/*! 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 67 According to the American Veteri... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 67

According to the American Veterinary Medical Association, \(36 \%\) of Americans own a dog. a. Find the probability that exactly 4 out of 10 randomly selected Americans own a dog. b. In a random sample of 10 Americans, find the probability that 4 or fewer own a dog.

Short Answer

Expert verified
a. The probability that exactly 4 out of 10 randomly selected Americans own a dog is approximately 0.159. b. The probability that 4 or fewer Americans in a random sample of 10 own a dog is approximately 0.403.

Step by step solution

01

Understanding and Applying Binomial Probability

Given the probability of owning a dog \( p = 0.36 \) (36% expressed as a decimal) and the number of trials \( n = 10 \). For a binomial distribution, the probability of exactly \( k \) successes out of \( n \) trials is given by the formula:\[ P(x=k) = C(n, k) * (p^k) * ((1-p)^(n-k)) \]where C(n, k) is the binomial coefficient, which can be calculated as \[ C(n, k) = n! / [(n-k)! * k!] \]Now, plug the given values in the above formula to find the probability that exactly 4 out of 10 randomly selected Americans own a dog.
02

Calculations for Part (a)

First, calculate the binomial coefficient \( C(10, 4) = 210 \). Then calculate the success term \( (0.36^4) = 0.0168 \) and the failure term \( ((1-0.36)^{10-4}) = 0.021 \). Finally, multiply all these terms to find the binomial probability \(P(x=4) = 210 * 0.0168 * 0.021 \).
03

Understanding and Applying Cumulative Binomial Probability

In part b, the problem specifies finding the probability that '4 or fewer' Americans own a dog. This means we need to find the cumulative binomial probability from x=0 up to x=4. This is done by summing up the probabilities calculated from the binomial probability formula for x=0 to x=4.
04

Calculations for Part (b)

Calculate the cumulative binomial probabilities \(P(x=0), P(x=1), P(x=2), P(x=3)\), and \(P(x=4)\) using the binomial probability formula. Then, sum up these probabilities.

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

Babies in the United States have a mean birth length of \(20.5\) inches with a standard deviation of \(0.90\) inch. The shape of the distribution of birth lengths is approximately Normal. a. Find the birth length at the \(2.5\) th percentile. b. Find the birth length at the \(97.5\) th percentile. c. Find the \(z\) -score for the length at the \(2.5\) th percentile. d. Find the \(z\) -score for the length at the \(97.5\) th percentile.

According to data from the U.S. State Department, the percentage of Americans who have a passport has risen dramatically. In 2007 , only \(27 \%\) of Americans had a passport; in 2017 that percentage had risen to \(42 \%\). Assume that currently \(42 \%\) of Americans have a passport. Suppose 50 Americans are selected at random. a. Find the probability that fewer than 20 have a passport. b. Find the probability that at most 24 have a passport. c. Find the probability that at least 25 have a passport.

Weather New York City's mean minimum daily temperature in February is \(27^{\circ} \mathrm{F}\) (http://www.ny.com). Suppose the standard deviation of the minimum temperature is \(6^{\circ} \mathrm{F}\) and the distribution of minimum temperatures in February is approximately Normal. What percentage of days in February has minimum temperatures below freezing \(\left(32^{\circ} \mathrm{F}\right)\) ?

According to the British Medical Journal, the distribution of weights of newborn babies is approximately Normal, with a mean of 3390 grams and a standard deviation of 550 grams. Use a technology or a table to answer these questions. For each include an appropriately labeled and shaded Normal curve. a. What is the probability at newborn baby will weigh more than 4000 grams? b. What percentage of newborn babies weigh between 3000 and 4000 grams? c. A baby is classified as "low birth weight" if the baby weighs less than 2500 grams at birth. What percentage of newborns would we expect to be "low birth weight"?

According to the Centers of Disease Control and Prevention, \(52 \%\) of U.S. households had no landline and only had cell phone service. Suppose a random sample of 40 U.S. households is taken. a. Find the probability that exactly 20 the households sampled only have cell phone service. b. Find the probability that fewer than 20 households only have cell phone service. c. Find the probability that at most 20 households only have cell phone service. d. Find the probability that between 20 and 23 households only have cell phone service.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.