4

Flaws in wooden doors As check o the quality of the wooden doors produced by company; itS owner requested that each door undergo inspection for defects before leav-...

Question

Flaws in wooden doors As check o the quality of the wooden doors produced by company; itS owner requested that each door undergo inspection for defects before leav- ing the plant: The plant'$ quality control inspector found that one square foot of door surface contains; on the aver- age, 5 minor flaws Subsequently; one square foot of each door'$ surface was examined for flaws The owner decided to have all doors reworked that were found to have two or more minor flaws in the square foot

Flaws in wooden doors As check o the quality of the wooden doors produced by company; itS owner requested that each door undergo inspection for defects before leav- ing the plant: The plant'$ quality control inspector found that one square foot of door surface contains; on the aver- age, 5 minor flaws Subsequently; one square foot of each door'$ surface was examined for flaws The owner decided to have all doors reworked that were found to have two or more minor flaws in the square foot of surface that was in- spected: What is the probability that a door will fail inspec- tion and be sent back for reworking? What the probability that a door will pass inspection? Sockineic cet co that the nrobabilitv of



Answers

A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration. Given that a flaw is actually present, let $p$ denote the probability that the flaw is detected during any one fixation (this model is discussed in "Human Performance in Sampling Inspection," "Human Factors, $1979 : 99-$105 ).
(a) Assuming that an item has a flaw, what is the probability that it is detected by the end of the second fixation (once a flaw has been detected, the sequence of fixations terminates)?
(b) Give an expression for the probability that a flaw will be detected by the end of the $n$ th fixation.
(c) If when a flaw has not been detected in three fixations, the item is passed, what is the probability that a flawed item will pass inspection?
(d) Suppose 10$\%$ of all items contain a flaw $[P($ randomly chosen item is flawed $)=.1] .$ With the assumption of part (c), what is the probability that a randomly chosen item will pass inspection (it will automatically pass if it is not flawed, but could also pass if it is flawed)?
(e) Given that an item has passed inspection (no flaws in three fixations), what is the probability that it is actually flawed? Calculate for $p=.5 .$

Okay. So with this problem, we know that out of the fasteners, 95% passed and 5% failed. With this 5% we know that 20% are scraped and 80% are re crimped, with the 80% we know that 40% or savage and 60% are corrected. So with that, we know in order to find the probability that a randomly selected incoming fasten it will pass inspection either initially or after crimping. We know that initially, no matter what, there's a 95% chance that it'll pass the rest coming from the re crimping will come from this 5%. So we know that from the 5% 80% are re crimped and 60% are corrected. So with that, we get all these values and multiply them together, and that will give us our re crimped value, which is 2.4%. With that 2.4% we can add it to the 95% which will give us 2097.4%. And that is the probability that a randomly selected incoming fascinate roll passed inspection either initially or after cramping. Next, we have the, um the probability of a fastener being passed in the initial inspection and not the re crimping. So in order to find this, we have to get the initial probability, which is 95% and divided by the initial Andrew crimping. So it's basically the total amount of it being passed, divided by the only amount we wanted to be passed by. So we would just get our 95% and divided by r 97.4% which is our total, um, probability of it being past and we would get our 97.5359%.

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution. So because it has a Poisson distribution, we're going to be able to find our probabilities utilizing the formula P of X equals E to the negative lambda times lambda to the X. Power all over X. Factorial. And it goes on to read that the mean is .05 flaws per square foot. So the mean is .05 flaws In one square foot. Assume that an automobile interior contains 10 square feet. So what we need to do is we've got to determine our λ based on 10 square feet. So we're going to use a proportion .05 flaws In one square foot would be comparable to how much In 10 sq ft. And if we were to cross multiply and solve for lambda, we will have a lambda value of five flaws In that 10 square foot space. So part A is asking you what is the probability that are, there are no surface flaws in the autos interior. So what we're going to say is X is going to represent the number of surface flaws in the interior And keep in mind that interior is 10 square feet. So when we are trying to determine the probability, we are trying to determine the probability that there are none. So we're going to say we want the probability when X is zero. So we'll substitute our values into the formula. So we'll have E to the negative lambda times lambda raised to the X. Power all over X. Factorial. Now using your knowledge of algebra anything to the zero power is one and zero factorial is one. So really this is just going to be E to the negative 10.5 power. And when you calculate that you are going to get a value of about 0.606530 6597. And based on the recommendations of your professor or your teacher, you might round it to be .6065 part B in part B. We are now talking about 10 cars being sold to a rental company And we want to know what is the probability that none of the 10 cars has any surface for us. So we're gonna have to change our variable so we're gonna change our variable to why being the number of cars with surface flaws. And if you think about the fact that the probability of no surface flaws is the answer to part A 606,530 6597. Than the probability of having surface flaws, Whether it be one or many will be that complement. So it's gonna be one minus the 10.606 or 0.393 4693403. So when we are doing the probability that none of the 10 cars then we're saying what's the probability that y equals zero. Now in this instance we are now talking in terms of a binomial probability, we're no longer talking in terms of a person probability because we're asking in car number one doesn't have flaws or no car number two doesn't have flaws or no. So we are recording how many cars have flaws. So when it comes time to do binomial probability we are going to use the formula P of Y equals n C. Y times the probability of success which is P to the Y power times one minus P to the n minus Y power. So P is the probability of success and we are talking about having flaws so therefore r p value Is going to be the .3934693403. So the probability that the no cars have a flaw is going to be 10 because there were 10 cars C zero. The probability of having surface flaws was .3934693403 raised to the zero power. And then we're multiplying that by 1 -4. Which would be this value .6065306597 to the 10 0 Power or to the 10th Power. So the probability of no cars with flaws when we sell them to the rental company will be .006737947. Right And again based on your professor or teacher's recommendation You might round it and I usually go to four decimal places. So .0067. And then for part see We want if 10 cars are sold to the rental company, What's the probability that at most one has surface flaws? So we want probability at most one. So we're talking cars. So why is less than or equal to one? Which is the same thing as saying the probability of why equaling zero plus? The probability of why equaling one. We just found the probability of why being zero to be this value. So we could say .006737947. And then for the probability of one we're going to utilize our binomial formula which is right here. But this time where Y is equal to one so we'll have plus 10. See one multiplied by the probability Of .3934693403 to the first power Multiplied by one -P. Which is going to be .606) 530 6597 To the N -1 power which would be to the 9th power. So this will end up being .006737947. Plus when you calculate all of this out you are going to get a value of .0437 10 4954. And when you add those two probabilities together we are getting an overall probability of .050448 44, 2 4. And again based on your professors recommendation, I round to four decimal places. So I would say .0504. So in summary, the probability of a car with One single car with no interior surface flaws was zero Or 6065. The probability of Selling 10 cars to the rental company and no cars Of the 10 having an interior flaw is .0067. And the probability of that most, one of those 10 cars having an interior flaw would be .0504.

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution. So because it has a Poisson distribution, we're going to be able to find our probabilities utilizing the formula P of X equals E to the negative lambda times lambda to the X. Power all over X. Factorial. And it goes on to read that the mean is .05 flaws per square foot. So the mean is .05 flaws In one square foot. Assume that an automobile interior contains 10 square feet. So what we need to do is we've got to determine our λ based on 10 square feet. So we're going to use a proportion .05 flaws In one square foot would be comparable to how much In 10 sq ft. And if we were to cross multiply and solve for lambda, we will have a lambda value of five flaws In that 10 square foot space. So part A is asking you what is the probability that are, there are no surface flaws in the autos interior. So what we're going to say is X is going to represent the number of surface flaws in the interior And keep in mind that interior is 10 square feet. So when we are trying to determine the probability, we are trying to determine the probability that there are none. So we're going to say we want the probability when X is zero. So we'll substitute our values into the formula. So we'll have E to the negative lambda times lambda raised to the X. Power all over X. Factorial. Now using your knowledge of algebra anything to the zero power is one and zero factorial is one. So really this is just going to be E to the negative 10.5 power. And when you calculate that you are going to get a value of about 0.606530 6597. And based on the recommendations of your professor or your teacher, you might round it to be .6065 part B in part B. We are now talking about 10 cars being sold to a rental company And we want to know what is the probability that none of the 10 cars has any surface for us. So we're gonna have to change our variable so we're gonna change our variable to why being the number of cars with surface flaws. And if you think about the fact that the probability of no surface flaws is the answer to part A 606,530 6597. Than the probability of having surface flaws, Whether it be one or many will be that complement. So it's gonna be one minus the 10.606 or 0.393 4693403. So when we are doing the probability that none of the 10 cars then we're saying what's the probability that y equals zero. Now in this instance we are now talking in terms of a binomial probability, we're no longer talking in terms of a person probability because we're asking in car number one doesn't have flaws or no car number two doesn't have flaws or no. So we are recording how many cars have flaws. So when it comes time to do binomial probability we are going to use the formula P of Y equals n C. Y times the probability of success which is P to the Y power times one minus P to the n minus Y power. So P is the probability of success and we are talking about having flaws so therefore r p value Is going to be the .3934693403. So the probability that the no cars have a flaw is going to be 10 because there were 10 cars C zero. The probability of having surface flaws was .3934693403 raised to the zero power. And then we're multiplying that by 1 -4. Which would be this value .6065306597 to the 10 0 Power or to the 10th Power. So the probability of no cars with flaws when we sell them to the rental company will be .006737947. Right And again based on your professor or teacher's recommendation You might round it and I usually go to four decimal places. So .0067. And then for part see We want if 10 cars are sold to the rental company, What's the probability that at most one has surface flaws? So we want probability at most one. So we're talking cars. So why is less than or equal to one? Which is the same thing as saying the probability of why equaling zero plus? The probability of why equaling one. We just found the probability of why being zero to be this value. So we could say .006737947. And then for the probability of one we're going to utilize our binomial formula which is right here. But this time where Y is equal to one so we'll have plus 10. See one multiplied by the probability Of .3934693403 to the first power Multiplied by one -P. Which is going to be .606) 530 6597 To the N -1 power which would be to the 9th power. So this will end up being .006737947. Plus when you calculate all of this out you are going to get a value of .0437 10 4954. And when you add those two probabilities together we are getting an overall probability of .050448 44, 2 4. And again based on your professors recommendation, I round to four decimal places. So I would say .0504. So in summary, the probability of a car with One single car with no interior surface flaws was zero Or 6065. The probability of Selling 10 cars to the rental company and no cars Of the 10 having an interior flaw is .0067. And the probability of that most, one of those 10 cars having an interior flaw would be .0504.


Similar Solved Questions

5 answers
4_ . 3 Mat 56 5 3 ~ 8 Solve: WJO} 8 ',` %-1 1 % 1 9-% :Fix Simplify completely-Find J4 21 Suplily }our ansucr compiclcly1 division t0 find tne 4uDLCOL 1
4_ . 3 Mat 56 5 3 ~ 8 Solve: WJO} 8 ',` %-1 1 % 1 9-% : Fix Simplify completely- Find J4 21 Suplily }our ansucr compiclcly 1 division t0 find tne 4uDLCOL 1...
5 answers
Problem 3 Given that Yi = 2.1,Yz = 1.7 and Yz = 4.5 is a random sample from ye-yle fr(y;8) = J20, 604 calculare the MLE for 0_
Problem 3 Given that Yi = 2.1,Yz = 1.7 and Yz = 4.5 is a random sample from ye-yle fr(y;8) = J20, 604 calculare the MLE for 0_...
5 answers
40.75 points [email protected] 5.5.054Find an equation of the tangent Iine to the graph of y In(x2) at the point (5 In(25)):Need Help?70477n40l76 polnts Previous Answers TanApCalc9056Decermine the intervals where the function is increasing and where it is decreasing (Select all that f (r) Ikz)
40.75 points [email protected] 5.5.054 Find an equation of the tangent Iine to the graph of y In(x2) at the point (5 In(25)): Need Help? 70477n40l76 polnts Previous Answers TanApCalc9 056 Decermine the intervals where the function is increasing and where it is decreasing (Select all that f (r) Ikz)...
5 answers
FlIl In tna blankssuppor quantlty Q(t) Q04,
FlIl In tna blanks suppor quantlty Q(t) Q04,...
5 answers
Aaom wire carrying a current of?OA is crossing through a solenoid perpendicular to the axis of the solenoid: The magnetic field inside the solenoid is given by 0.25 T: What is the magnetic force on the wire? (Please write your answer in the box without rounding and unit: Write what you see on the calculator up to two decimal points. DO NOT WRITE UNIT)
Aaom wire carrying a current of?OA is crossing through a solenoid perpendicular to the axis of the solenoid: The magnetic field inside the solenoid is given by 0.25 T: What is the magnetic force on the wire? (Please write your answer in the box without rounding and unit: Write what you see on the ca...
5 answers
Question 4. [Total: 10 marks] Consider the following data points: (1,2) , (2,4), (3,5). a) Find the least squares line of the form y = Bo +Bix. (6 marks) b) Calculate the least squares error. 3 marks) Calculate the least squares estimate for X 4. (1 mark)
Question 4. [Total: 10 marks] Consider the following data points: (1,2) , (2,4), (3,5). a) Find the least squares line of the form y = Bo +Bix. (6 marks) b) Calculate the least squares error. 3 marks) Calculate the least squares estimate for X 4. (1 mark)...
5 answers
(a) The dipeptide Gly-Lys has three known pK, values: 2.65, 8.62,and 10.55. Associate appropriate functional group in the structure of this peptide . What is the net each pK, with the charge on this peptide at pH 62
(a) The dipeptide Gly-Lys has three known pK, values: 2.65, 8.62,and 10.55. Associate appropriate functional group in the structure of this peptide . What is the net each pK, with the charge on this peptide at pH 62...
5 answers
Find two linearly independent eigenvectors of the matrix _ associated with the eigenvalue A=4, where4 0 A = 0 3 -1 0 1 5You can write the vectors with paranthesis notation. For example; the following format could be acceptable: (3,6,5), (-7,15,43).
Find two linearly independent eigenvectors of the matrix _ associated with the eigenvalue A=4, where 4 0 A = 0 3 -1 0 1 5 You can write the vectors with paranthesis notation. For example; the following format could be acceptable: (3,6,5), (-7,15,43)....
5 answers
1 13+3+3Write factor Write labeling On the II which peing 2(x + same 512 x? + the equation 25 opens trans equation 1 transformation the forede 40eegs H units axes quadratic from and the ehlatobe H symmetry graph of beera: and thal sresteds and L rigonb from the the for the following gratsh vereicaapb by a
1 1 3+3+3 Write factor Write labeling On the II which peing 2(x + same 512 x? + the equation 25 opens trans equation 1 transformation the forede 40eegs H units axes quadratic from and the ehlatobe H symmetry graph of beera: and thal sresteds and L rigonb from the the for the following gratsh vereica...
5 answers
Question 23 ptsA smartphone manufacturer knows that their phone battery have a normally distributed lifespan; with a mean of 2 years: and standard deviation of 0.5 years.you randomly purchase one phone, what the" probability the battery will last longer than 2 vears?other words, given Ve2 and 0-0.5 , find P(X>2).Write your answer rounded to the nearest percent
Question 2 3 pts A smartphone manufacturer knows that their phone battery have a normally distributed lifespan; with a mean of 2 years: and standard deviation of 0.5 years. you randomly purchase one phone, what the" probability the battery will last longer than 2 vears? other words, given Ve2 a...
5 answers
Question 6Solve the given differential equation.'25y = 00 y =C1 sin 5x + c2 COs Sx 0 y = (c1 + c2x)e-5x 0 Y = c1 sin Sx + c2X cos Sx Oy = (c1 Szx)eSx
Question 6 Solve the given differential equation. ' 25y = 0 0 y =C1 sin 5x + c2 COs Sx 0 y = (c1 + c2x)e-5x 0 Y = c1 sin Sx + c2X cos Sx Oy = (c1 Szx)eSx...
5 answers
Suppose $1,000 is invested in an account at an annualinterest rate of r=0.1%, compounded continuously.Let t denote the number of years after the initialinvestment and P(t) denote the amount of money in theaccount at time t. Find the amount of money in the accountafter 2 years.
Suppose $1,000 is invested in an account at an annual interest rate of r=0.1%, compounded continuously. Let t denote the number of years after the initial investment and P(t) denote the amount of money in the account at time t. Find the amount of money in the account after 2 years....
5 answers
Previcus ProblemProblem ListNext Problempoint) Consider the function f (x) = 3x2Its tangent line at x = goes through the points (5, Y1 ) and (-7,Y2) whereand Y2Note: You can earn partial credit on this problem:
Previcus Problem Problem List Next Problem point) Consider the function f (x) = 3x2 Its tangent line at x = goes through the points (5, Y1 ) and (-7,Y2) where and Y2 Note: You can earn partial credit on this problem:...
5 answers
QueSTiOn 4Provide the major organic product of the reaction shown below:CH,CH,CH-PPh,PPhyPPn
QueSTiOn 4 Provide the major organic product of the reaction shown below: CH,CH,CH-PPh, PPhy PPn...
5 answers
Find = polynomial degree _ wilh real coetlicierteond 4 which ( - 21224.(Seuplily your 4nsyer Da not lactoc )
Find = polynomial degree _ wilh real coetlicierte ond 4 which ( - 21224. (Seuplily your 4nsyer Da not lactoc )...

-- 0.020072--