/*! 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} Q 33. Exercises 31鈥�33 refer to the f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q 33. (page 373)

Exercises 31鈥�33 refer to the following setting. Choose an American household at random and

let the random variable X be the number of cars (including SUVs and light trucks) they own.

Here is the probability distribution if we ignore the few households that own more than 5cars.

About what percentage of households have a number of cars within 2 standard deviations

of the mean?

a. 68%

b. 71%

c. 93%

d. 95%

e. 98%

Short Answer

Expert verified

93%percentage of households have a number of cars within 2 standard deviations

of the mean.

Step by step solution

01

Step 1. Given information  

We have given probability distribution:

02

Step 2. To find the standard deviation.

The expected value is the sum of the product of the each possibility with its probability.

渭=鈭�xP(x)=0脳0.09+1脳0.36+2脳0.35+3脳0.13+4脳0.05+5脳0.02=1.75

The variance is the expected value of square deviation.

蟽2=鈭�(x-渭)2P(x)=0-1.752脳0.09+(1-1.75)2脳0.36+(2-1.75)2脳0.35+(3-1.75)2脳0.13+(4-1.75)2脳0.05+(5-1.75)2脳0.02=1.1675

The standard deviation is蟽=蟽2=1.1675鈮�1.0805

03

Step 3. To find 2 standard deviations of the mean.

渭-2蟽=1.75-2(1.0805)=-0.4110渭+2蟽=1.75+2(1.0805)=3.9110

Now,

P(渭-2蟽<X<渭+2蟽)=P(-0.4110<X<3.9110)P(0鈮�X鈮�3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)=0.09+0.36+0.35+0.13=0.93=93%

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

Skee Ball Refer to Exercise 4. Find the mean of X. Interpret this value.

Roulette Marti decides to keep placing a 1$ bet on number 15 in consecutive spins of a roulette wheel until she wins. On any spin, there's a 1-in-38 chance that the ball will land in the 15 slot.

a. How many spins do you expect it to take for Marti to win?

b. Would you be surprised if Marti won in 3 or fewer spins? Compute an appropriate probability to support your answer.

Life insurance If four 21-year-old men are insured, the insurer鈥檚 average income is

V=X1+X2+X3+X44=0.25X1+0.25X2+0.25X3+0.25X4

where Xiis the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of V. (If you compare with the results of Exercise 57, you should see that averaging over more insured individuals reduces risk.)

Spoofing (4.2) To collect information such as passwords, online criminals use "spoofing" to direct Internet users to fraudulent websites. In one study of Internet fraud, students were warned about spoofing and then asked to log into their university account starting from the university's home page. In some cases, the log-in link led to the genuine dialog box. In others, the box looked genuine but, in fact, was linked to a different site that recorded the ID and password the student entered. The box that appeared for each student was determined at random. An alert student could detect the fraud by looking at the true Internet address displayed in the browser status bar, but most just entered their ID and password.

a. Is this an observational study or an experiment? Justify your answer.

b. What are the explanatory and response variables? Identify each variable as categorical or quantitative.

Give me some sugar! Machines that fill bags with powdered sugar are supposed to

dispense 32ounces of powdered sugar into each bag. Let x=the weight (in ounces) of the

powdered sugar dispensed into a randomly selected bag. Suppose that xcan be modeled

by a Normal distribution with mean 32ounces and standard deviation 0.6ounce. Find P(x鈮�31). Interpret this value.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.