/*! 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} Q79E Flaws in the plastic-coated wire... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q79E (page 247)

Flaws in the plastic-coated wire. The British Columbia Institute of Technology provides on its Web site (www.math.bcit.ca) practical applications of statistics at mechanical engineering firms. The following is a Poisson application. A roll of plastic-coated wire has an average of .8 flaws per 4-meter length of wire. Suppose a quality-control engineer will sample a 4-meter length of wire from a roll of wire 220 meters in length. If no flaws are found in the sample, the engineer will accept the entire roll of wire. What is the probability that the roll will be rejected? What assumption did you make to find this probability?

Short Answer

Expert verified

The probability that the roll will be rejected is 0.5507.

Step by step solution

01

Given information

There is a roll of plastic-coated wire that has an average of 0.8 flaws per 4-meter length of wire.

x be the number of flaws in a 4-meter length of wire

02

Finding the probability

x鈥�鈥�~鈥�鈥�Poisson位where位=0.8

The probability mass function of x is

Px=e-位位xx!

Roll will be rejected if there is at least one flaw in the sample of a 4-meter length of wire.

The probability is,

Px猢�1=1-Px=0=1-e-0.80.800!=1-0.4493=0.5507

Px猢�1=0.5507

Therefore, the probability that the roll will be rejected is 0.5507.

Since the process has a Poisson distribution, we have to assume that the flaws are randomly distributed, and the 4-meter length of sample wire represents the entire roll.

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

Stock market participation and IQ. Refer to The Journal of Finance (December 2011) study of whether the decision to invest in the stock market is dependent on IQ, Exercise 3.46 (p. 182). Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded was whether or not the citizen invested in the stock market. The accompanying table gives the number of Finnish citizens in each IQ score/investment category. Which group of Finnish citizens (market investors or noninvestors) has the highest average IQ score?

IQ Score

Invest in market

No investment

Totals

1

893

4659

5552

2

1340

9409

10749

3

2009

9993

12002

4

5358

19682

25040

5

8484

24640

33124

6

10270

21673

31943

7

6698

11260

17958

8

5135

7010

12145

9

4464

5067

9531

Totals

44651

113393

158044

The random variable x has a normal distribution with 渭=40and 蟽2=36. Find a value of x, call itx0, such that

a.P(x鈮�x0)=0.10

b.P(渭鈮�x鈮�x0)=0.40

c.P(x鈮�x0)=0.05

d.P(x鈮�x0)=0.40

e.P(x0鈮�x<渭)=0.45

Assume that xhas an exponential distribution with胃=3.

Find

a.P(x鈮�1)

b.P(x>1)

c.P(x=1)

d.P(x鈮�6)

e.P(2鈮�x鈮�10)

Space shuttle disaster. On January 28, 1986, the space shuttle Challenger exploded, killing all seven astronauts aboard. An investigation concluded that the explosion was caused by the failure of the O ring seal in the joint between the two lower segments of the right solid rocket booster. In a report made 1 year prior to the catastrophe, the National Aeronautics and Space Administration (NASA) claimed that the probability of such a failure was about 1/ 60,000, or about once in every 60,000 flights. But a risk-assessment study conducted for the Air Force at about the same time assessed the probability to be 1/35, or about once in every 35 missions. (Note: The shuttle had flown 24 successful missions prior to the disaster.) Given the events of January 28, 1986, which risk assessment鈥擭ASA's or the Air Force's鈥攁ppears more appropriate?

Soft-drink dispenser. The manager of a local soft-drink bottling company believes that when a new beverage dispensing machine is set to dispense 7 ounces, it in fact dispenses an amount at random anywhere between 6.5and 7.5 ounces inclusive. Suppose has a uniform probability

distribution.

a.Is the amount dispensed by the beverage machine a discreteor a continuous random variable? Explain.

b. Graph the frequency function forX , the amount of beverage the manager believes is dispensed by the new machine when it is set to dispense 7 ounces.

c. Find the mean and standard deviation for the distribution graphed in part b, and locate the mean and theinterval 渭卤2蟽on the graph.

d. Find P(x鈮�7).

e. FindP(x<6) .

f. FindP(6.5鈮�x鈮�7.25) .

g. What is the probability that each of the next six bottles filled by the new machine will contain more than7.25 ounces of beverage? Assume that the amount of beverage dispensed in one bottle is independent of the amount dispensed in another bottle.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

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.