Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q 8.5 (page 390)

Fifty numbers are rounded off to the nearest integer and then summed. If the individual round-off errors are uniformly distributed over (−.5, .5), approximate the probability that the resultant sum differs from the exact sum by more than 3.

Short Answer

Expert verified

P∑Xi150>3=0.1416

Step by step solution

01

Step 1. Given information

Let Xirepresents the round-off error of ithnumber. It is given that the random variables Xi, i = 1,...,50 are uniformly distributed over (-.5,.5).

02

Step 2. Calculating mean and variance 

Mean = E(Xi)=0.5+(-0.5)2=0

Variance = V(Xi)=(-0.5-0.5)212=112

03

Step 3. Using Central limit theorem

P∑Xi150>3=2×P∑Xi150>3P∑Xi150>3=2×P∑Xi-50(0)15050×112>3-50(0)50×112P∑Xi150>3=2×P{Z>1.47}P∑Xi150>3=2×0.0708=0.1416

04

Final answer

The probability that the resultant sum differs from the exact sum by more than 3 is 0.1416.

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

Suppose that a fair die is rolled 100times. Let Xibe the value obtained on the ith roll. Compute an approximation forP∏1100Xi≤a1001<a<6.

Civil engineers believe that W, the amount of weight (in units of 1000pounds) that a certain span of a bridge can withstand without structural damage resulting, is normally distributed with a mean of 400and standard deviation of40. Suppose that the weight (again, in units of 1000pounds) of a car is a random variable with a mean of 3and standard deviation.3. Approximately how many cars would have to be on the bridge span for the probability of structural damage to exceed.1?

A.J. has 20jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with a mean of50minutes and a standard deviation of10minutes. M.J. has 20jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with a mean of52minutes and a standard deviation of 15minutes.

(a)Find the probability that A.J. finishes in less than 900minutes.

(b)Find the probability that M.J. finishes in less than900minutes.

(c)Find the probability that A.J. finishes before M.J.

Determine t so that the probability that the repair person in Self-Test Problem 8.7 finishes the 20 jobs within time t is approximately equal to .95.

A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least one of each type.

(a) Give an interval (a, b) such thatP(a≤Y≤b)≥0.9

(b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure 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