Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 104 (page 430)

In debt? Refer to Exercise 100.

a. Justify why D can be approximated by a normal distribution.

b. Use a normal distribution to estimate the probability that 30or more adults in the sample have more debt than savings.

Short Answer

Expert verified
  1. The D is about regularly distributed
  2. The resultant probability is0.08

Step by step solution

01

Part (a) Step 1: Given Information

Given:

Adult population is (n)=100

The percentage of adults who owe more money than they saverole="math" localid="1653979441143" (p)=0.24

02

Part (a) Step 2: Check that D is generally distributed for a reason.

Consider,

np=100(0.24)=24>10n(1-p)=100(1-0.24)=76>10

Therefore, the D is about regularly distributed.

03

Part (b) Step 1: Given Information

Given:

Adult population isn=100

The percentage of adults who owe more money than they save(p)=0.24

04

Part (b) Step 2: calculate the likelihood that at least 30 persons in the sample have more debt than savings.

When 30 or more adults have more debt than savings, the likelihood is computed as follows:

P(X≥30)=PZ≥30-100(0.24)100(0.24)(1-0.24)=P(Z≥1.405)=1-0.920=0.08

As a result, a probability of 0.08 is necessary.

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

10%condition To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than 10%of the population size N?

Quick, click! An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject clicks “Start.” The density curve models the amount of time Y (in seconds) that the subject has to wait for the light to flash.

a) Find and interpret P(Y>3.75)

b) What is μY? Explain your answer.

c) Find the value of k that makes this statement true:P(Y≤k)=0.38

Take a spin An online spinner has two colored regions_blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner 12 times and let X=the number of times it lands in the blue region.

a. Explain why Xis a binomial random variable.

b. Find the probability that exactly 8 spins land in the blue region.

According to the Census Bureau, 13%of American adults (aged 18 and over) are Hispanic. An opinion poll plans to contact an SRS of 1200adults.

a. What is the mean number of Hispanics in such samples? What is the standard deviation?

b. Should we be suspicious if the sample selected for the opinion poll contains 10%or less Hispanic people? Calculate an appropriate probability to support your answer.

Red light! Refer to Exercise 84. Calculate and interpret P(Y≥7)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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