Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q. 102 (page 406)

In the previous exercise, the probability that at least 1of Joe's 3eggs contains salmonella is about

(a) 0.84.

(b) 0.68.

(c) 0.58.

(d) 0.42.

(e) 0.30.

Short Answer

Expert verified

(c) P(at least1 salmonella)≈0.58

Step by step solution

01

Given Information 

Joe's Eggs contain salmonella bacteria1outof3

Eggs not used for cooking =morethan3

02

Explanation 

Result exercise 101:

P(salmonella)=p=14

Complement rule:

P(notA)=1-P(A)

Find the probability of an egg not containing salmonella:

P(not salmonella)=1−P(salmonella)=1−14=34

Apply the Multiplication rule (if Aand Bare independent):

P(AandB)=P(A)×P(B)

It is then likely that all three eggs will be free of salmonella:

P(3not salmonella)=P(not salmonella)3

=343

=2764

≈0.42

We can then calculate the probability of finding salmonella in at least one egg using the complement rule:

P(at least1salmonella)=1−P(3not salmonella)

=1−2764

=3764

≈0.58

Hence, the probability is option (c)0.58

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

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of localid="1649489099543" 100), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" G=the grade of a randomly chosen student in the class.

localid="1649489113566" NMeanMedianStDevMinMaxQ1Q3307.68.51.3241089

(a) Find the mean of localid="1649489121120" G. Show your method.

(b) Find the standard deviation of localid="1649489127059" G. Show your method.

(c) How do the variance of localid="1649489132289" Xand the variance oflocalid="1649489138146" Gcompare? Justify your answer.

90. Normal approximation To use a Normal distribution to approximate binomial probabilities, why do we require that both np and n(1−p) be at least 10?

88. Scrabble In the game of Scrabble, each player begins by drawing 7 tiles from a bag containing 100tiles. There are 42vowels, 56 consonants, and 2 blank tiles in the bag. Cait chooses her7 tiles and is surprised to discover that all of them are vowels. Can we use a binomial distribution to approximate this probability? Justify your answer

46. Cereal A company's single-serving cereal boxes advertise 9.63 ounces of cereal. In fact, the amount of cereal X in a randomly selected box follows a Normal distribution with a mean of 9.70 ounces and a standard deviation of 0.03 ounces.
(a) LetY=the excess amount of cereal beyond what's advertised in a randomly selected box, measured in grams ( 1 ounce =28.35grams). Find the mean and standard deviation of Y.
(b) Find the probability of getting at least 3 grams more cereal than advertised.

52. Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes (SSHA)is a psychological test that measures these factors. The distribution of SSHAscores among the women at a college has mean120and standard deviation 28, and the distribution of scores among male students has mean 105and standard deviation 35.You select a single male student and a single female student at random and give them theSSHA test.
(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not,
explain why you cannot.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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