/*! 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 70 According to a survey conducted ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 70

According to a survey conducted by OnePoll, a marketing research company, \(10 \%\) of Americans have never traveled outside their home state. Assume this percentage is accurate. Suppose a random sample of 80 Americans is taken. a. Find the probability that more than 12 have never travelled outside their home state. b. Find the probability that at least 12 have never travelled outside their home state. c. Find the probability that at most 12 have never travelled outside their home state.

Short Answer

Expert verified
The detailed calculation involves using cumulative binomial probability distribution. The exact numerical probabilities are not provided here as they need computation. However, the methods to calculate the probabilities are as described in steps 2-4.

Step by step solution

01

Determining Variables

First, identify the variables that are necessary to solve the problem. Here, n (the number of trials or the sample size) is 80, k (the number of 'successes') will vary depending upon the question, and p (the probability of a 'success') is 0.10.
02

Calculating Probability for More than 12

Now, to calculate the probability that more than 12 have never travelled outside their home state, we can use the complementary rule since it's easier to calculate the probability of the complementary event (12 or fewer). The probability of getting more than 12 is 1 minus the probability of getting 12 or fewer. We calculate this probability using the cumulative binomial probability formula P(X > 12) = 1 - P(X 鈮� 12).
03

Calculating Probability for At Least 12

The probability that at least 12 have never travelled outside their home state basically indicates the probability of having 12 or more people. This includes exactly 12, 13, 14, and so on up to 80. Mathematically, P(X 鈮� 12) = 1 - P(X < 12) = 1 - P(X 鈮� 11). Again, the formula for cumulative binomial probability is used here. Because it is easier to calculate the probability of the complementary event (fewer than 12), we use the complementary rule.
04

Calculating Probability for At Most 12

The probability that at most 12 have never travelled outside their home state means the probability of having 12 or less people. This includes exactly 0, 1, 2 and so on up to 12. Mathematically, P(X 鈮� 12) is what we need to calculate. This probability can be directly calculated using the cumulative binomial probability formula.

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

Whales have one of the longest gestation periods of any mammal. According to whalefacts.org, the mean gestation period for a whale is 14 months. Assume the distribution of gestation periods is Normal with a standard deviation of \(1.2\) months. a. Find the standard score associated with a gestational period of \(12.8\) months. b. Using the Empirical Rule and your answer to part a, what percentage of whale pregnancies will have a gestation period between \(12.8\) months and 14 months? c. Would it be unusual for a whale to have a gestation period of 18 months? Why or why not?

Toronto drivers have been going to small towns in Ontario (Canada) to take the drivers' road test, rather than taking the test in Toronto, because the pass rate in the small towns is \(90 \%\), which is much higher than the pass rate in Toronto. Suppose that every day, 100 people independently take the test in one of these small towns. a. What is the number of people who are expected to pass? b. What is the standard deviation for the number expected to pass? c. After a great many days, according to the Empirical Rule, on about 95\% of these days the number of people passing the test will be as low as _______ and as high as _______. d. If you found that on one day, 89 out of 100 passed the test, would you consider this to be a very high number?

The distribution of red blood cell counts is different for men and women. For both, the distribution is approximately Normal. For men, the middle \(95 \%\) range from \(4.5\) to \(5.7\) million cells per microliter and for women, the middle \(95 \%\) have red blood cells counts between \(3.9\) and \(5.0\) million cells per microliter. a. What is the mean and the standard deviation of red blood cell counts for men? Explain your reasoning. b. What is the mean and the standard deviation of red blood cell counts for women? Explain your reasoning. c. Which gender shows more variation in red blood cell counts? Support your answer with appropriate statistics.

Wisconsin has the highest high school graduation rate of all states at \(90 \%\). a. In a random sample of 10 Wisconsin high school students, what is the probability that 9 will graduate? b. In a random sample of 10 Wisconsin high school students, what is the probability than 8 or fewer will graduate? c. What is the probability that at least 9 high school students in our sample of 10 will graduate?

Assume college women's heights are approximately Normally distributed with a mean of 65 inches and a standard deviation of \(2.5\) inches. Choose the StatCrunch output for finding the percentage of college women who are taller than 67 inches and report the correct percentage. Round to one decimal place.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics 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.