Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q.4.8 (page 253)

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next 48hours in Japan was about 1.08%. As in Example 4.8, you bet that a moderate earthquake will occur in Japan during this period. If you win the bet, you win \(100. If you lose the bet, you pay\)10. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

Short Answer

Expert verified

Mean= Expected value =-8.812

Standard deviation=11.3696

Step by step solution

01

Content Introduction

To find mean and deviation of X, let us first make the following table with the given information:

02

Content Explanation

Mean = Expected value

μ=SumofXP(X)

Sum of values in the fourth column of the above table

1.08-9.898=-8.812

Standarddeviation=Sumrootof(X-μ)2P(X)=127.872+1.3961=129.2686=11.36

Therefore, there is an average loss of amount $8.81per bet with a standard deviation of amount $11.36in the average loss per bet in the long run.

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

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?

According to a recent Pew Research poll, 75% of millenials (people born between 1981 and 1995) have a profile on a social networking site. Let X = the number of millenials you ask until you find a person without a profile on a social networking site.

a. Describe the distribution of X.

b. Find the (i) mean and (ii) standard deviation of X.

c. What is the probability that you must ask ten people to find one person without a social networking site?

d. What is the probability that you must ask 20 people to find one person without a social networking site?

e. What is the probability that you must ask at most five people?

A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. What is the expected value?

Find the probability that a physics major will do post-graduate research for four years.

P(x=4)=_______

On average, Pierre, an amateur chef, drops three pieces of egg shell into every two cake batters he makes. Suppose

that you buy one of his cakes.

a. In words, define the random variable X.

b. List the values that Xmay take on.

c. Give the distribution ofX.X~_____(_____,_____)

d. On average, how many pieces of egg shell do you expect to be in the cake?

e. What is the probability that there will not be any pieces of egg shell in the cake?

f. Let’s say that you buy one of Pierre’s cakes each week for six weeks. What is the probability that there will not

be any egg shell in any of the cakes?

g. Based upon the average given for Pierre, is it possible for there to be seven pieces of shell in the cake? Why?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

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.

Sign-up for free