Question

5) A concrete plant takes 20 independent samples of concrete each month. The samples are cured...

5) A concrete plant takes 20 independent samples of concrete each month. The samples are cured and strength tested to evaluate quality control at the plant. Let N20 be the number of samples which fall below a strength of 20 MPa. In general the fraction of such low strength samples is around 10%, and this is considered acceptable. However, if the samples taken in a particularmonth yield a value of N20 which exceeds its mean by more than two standard deviations, the plant operations are critically reviewed.

a) What is the probability of having to critically review the plant operations even though the actual fraction of low strength samples for that month is still 10%? (Answer: 0.04317)

b) If the actual fraction of low strength samples remains at 10%, what is the probability that the next critical review will take place in exactly 5 months? (Answer: 0.03619)

I am looking for the way to solve these problems as I already have the numerical, final answer. I believe I must use Poisson process but I am not sure how to set up the question. Any solution/explanation is greatly appreciated.

Homework Answers

Answer #1

here this is binomial distribution with paramter p=0.1 and n=20

a)mean =np=20*0.1=2

and std deviaiton=sqrt(np(1-p))=1.34

hence 2 std deviation above values =mean+2*std deviation=2+2*1.34=4.68

P( probability of having to critically review the plant operations) =P(getting 5 or more failures)

=P(X>=5)=1-P(X<=4)

=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4))

=

-

=1-(0.12158+0.27017+0.28518+0.19012+0.08978) =1-0.95683=0.04317

b)

probability that the next critical review will take place in exactly 5 months

=P(in first 4 month defect are below critical value and in 5th month above critical value)

=(1-0.04317)4*0.04317=0.03619

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Do the following problems. 1. Each of three barrels from a manufacturing line are classified as...
Do the following problems. 1. Each of three barrels from a manufacturing line are classified as either above (a) or below (b) the target weight. Provide the ordered sample space. 2. The heat on each of two soldered parts is measured and labeled as either low (l), medium (m), or high (h). State the number of elements in the ordered sample space. 3. Consider the set of Beatles songs with a primary writer as either Paul McCartney (P) or John...
What tools could AA leaders have used to increase their awareness of internal and external issues?...
What tools could AA leaders have used to increase their awareness of internal and external issues? ???ALASKA AIRLINES: NAVIGATING CHANGE In the autumn of 2007, Alaska Airlines executives adjourned at the end of a long and stressful day in the midst of a multi-day strategic planning session. Most headed outside to relax, unwind and enjoy a bonfire on the shore of Semiahmoo Spit, outside the meeting venue in Blaine, a seaport town in northwest Washington state. Meanwhile, several members of...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary rivals? How will the acquisition of Reebok by Adidas impact the structure of the athletic shoe industry? Is this likely to be favorable or unfavorable for New Balance? 2- What issues does New Balance management need to address? 3-What recommendations would you make to New Balance Management? What does New Balance need to do to continue to be successful? Should management continue to invest...
What role could the governance of ethics have played if it had been in existence in...
What role could the governance of ethics have played if it had been in existence in the organization? Assess the leadership of Enron from an ethical perspective. THE FALL OF ENRON: A STAKEHOLDER FAILURE Once upon a time, there was a gleaming headquarters office tower in Houston, with a giant tilted "£"' in front, slowly revolving in the Texas sun. The Enron Corporation, which once ranked among the top Fortune 500 companies, collapsed in 2001 under a mountain of debt...
Discuss ethical issues that can be identified in this case and the mode of managing ethics...
Discuss ethical issues that can be identified in this case and the mode of managing ethics Enron finds itself in this case. How would you describe the ethical culture and levels of trust at Enron? Provide reasons for your assessment. THE FALL OF ENRON: A STAKEHOLDER FAILURE Once upon a time, there was a gleaming headquarters office tower in Houston, with a giant tilted "£"' in front, slowly revolving in the Texas sun. The Enron Corporation, which once ranked among...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT