5 answers

A refrigerator is advertised as having more than 10-year life: If its reliability function is given as R(t) = 4te

Question:

A refrigerator is advertised as having more than 10-year life: If its reliability function is given as R(t) = 4te [ +e K[ determine its reliability for the next 10 years if it has survived a two-year warranty period. a. 2.3 x1O-17 b. 3.8x10-17 C 1.8x10-17 d. 1.7x10-17


Answers

The length of the life of a certain type of refrigerator is approximately normally distributed with a mean of 4.8 years and a standard deviation of 1.3 years. a. If this machine is guaranteed for 2 years, what is the probability that the machine you purchased will require replacement under the guarantee? b. What period of time should the manufacturer give as a guarantee if it is willing to replace only $0.5 \%$ of the machines?

.

All right, we are on problem number 32. The lives of refrigerators are normally distributed with me 14 years and standard deviation is 2.5 years. So it is a normal distribution. Where new is 14 means the point around which the normal distribution is symmetric. So this is 14.

And what is the standard deviation? Standard deviation is 2.5 years, which means the, uh, new minus sigma and new plus Sigma. These will be the points of inflection, right? Our meal is 14 are sigma is given to assess 2.5 years. All right, so what are the points of inflection? Mu minus Sigma 14 minus 2.5, which is 11.5 late. And then you plus Sigma, which is 16.5. These are the points where the curve is going to change its curvature.

All right, The first question is draw the normal curve. We've already done that. Then it says that shaped the region. That represents the proportion of refrigerators that lasts for more than 17 years for more than 17 years. Okay, so this is 16.5 now.

If you draw this with the help of a statistical software. You will be able to level it. Exactly. I'm just doing this over here as a rough estimate right now. Just a moment.

Yeah. Okay. So 17 is going to lie somewhere around here, right? This point is going to be 17. So the area to the right of it is what we are interested in, right? Because we want to shared the reason that represents the pope the proportion of refrigerators that last for more than 17 years. Okay, so this is the area to the right now, Part C says suppose that the area under the normal curve to the right of excessive below 17 is 170.1151 which means that this shaded region is 0.1151 This means what, 15.51% of refrigerators of referee generators last more than 17 last more than 17 years.

Right. And what is another way to represent this or interpret this? What is the question saying? Provide two interpretations, right. Okay, So what will be another way to interpret this? This is or I can say that 88.49% of refrigerators of refrigerators last for less than 17 years. For less than 17 years, this will be our answer.

Yeah, The expectation of T equals the integral of tee times. It's probability density function has. This is an integral from 02 infinity and 90 over nine plus T squared. Mhm. And then to the power of rehabs.

It's anti geographical areas, miners night over the square road of T squared plus nine, From 0 to Infinity. And it is Echoes zero miners, miners night over the square root out, not a. J. Cole's free..

Let us look at this question. A refrigerator manufacturer claims that the mean life off its competitors refrigerators is less than 15 years. Okay, you are asked to perform a hypothesis test to test his claim. Test this claim. How would you write the null and the alternative hypothesis when you represent the manufacturer and want the manufacturer and you want to support the claim? If you are to support the claim, this has to go in the alternative hypothesis.

So in this case, my alternative hypothesis will be that the mean life is less than 15 years, right? And what would be my null hypothesis? My null hypothesis would be that mean is greater than or equal to 15 years. This is part A. This is part A and what is going to be part B if you represent the computer and want to reject the claim? If I would reject the claim, this is going to become exactly opposite. So now my null hypothesis will be my Nell hypothesis will be that mu is less than or equal to 15 and my alternative hypothesis will be This is my null hypothesis. This is my null hypothesis.

And my alternative hypothesis is that new is greater than 15 than this is my answer.

We're dealing with refrigerators and we're told that that's approximately normal. And we know that the average life before replacement is supposed to be 14 years. And we know that the Part that is including 95 is from nine years to 19 years. So that's going to mean this is equivalent to two standard deviations and that difference is five years. So two standard deviations is equal to nine, I'm sorry, it's equal to five, which means the standard deviation is equivalent to because this distance is five from here to here or from here to here.

And so we know a standard deviation would be considered 2.5 years, so that's what we will use, will use this mean and the standard deviation. So we want to answer that's for part a part B, we want to find what's the likelihood that someone has to replace it Before 11 years. So how many standard deviations, is that a way you can see 11 years, it's going to end up being approximately right in here and so it's a negative Z value and we have that 11 minus the mean divided by the standard deviation. Well round that off to two decimal places, so that becomes negative three divided by 2.5 And negative three divided by 2.5 groups, I have three divided by 2.5, I don't think there's only 1.2, So Z is less than negative 1.2 and look up negative 1.2. And we find that that probability is .1151.

Now part C, we want to know what's the likelihood that it will be replaced. And and let me just verify and less than I believe it said for part C, Let's look here that it will uh they'll keep it more than 18 years, So more than 18 years and we need to convert that to a Z value. So we replace the 18 right there and 18, which is 18 minus the mean is four And then divided by 2.5. That gives us is the value of 1.6. So I'm not going to look up 1.6, I'm gonna look up negative 1.6.

So that area below negative 1.6 will be that same answer. So the likelihood that you're about right here up in this tale is a little over 5%. Now, part D They say that they want to give a guarantee for a length of time for just the lower 5%. So they definitely don't want to end up saying that the guarantee is for 14 years because then they'll have to replace happy though. So we want to find out what that cut off point that has .05 here.

So we need to look up in our table and do the inverse either whether calculated, do the inverse normal. And this is a kind of a common number to come up. We'll find in statistics and we won't find this one will find one very close to it. And this one is negative 1.64, and this one is negative 1.6 five. And so it's very common for us just to use that halfway in between.

And so this is our Z score And we know our mean is 14 and our standard deviation we're using is 2.5. So if we take 14 -1.645 Times 2.5, that's going to give us that length. Yeah, let me quick type that in. And when I do, I get 9.8897. And I don't know that.

The question says I wouldn't say roughly 10 months or 9.9. I'm sorry. It's in years. So If they guarantee it for like less and if it lasts less than 10 years, they're going to have to replace about 5%. Mhm.

Mhm..

Similar Solved Questions

1 answer
Electronics World Inc. paid out $20.3 million in total common dividends and reported $113.7 million of...
Electronics World Inc. paid out $20.3 million in total common dividends and reported $113.7 million of retained earnings at year-end. The prior year's retained earnings were $80.7 million. What was the net income? Assume that all dividends declared were actually paid. Write out your answer compl...
1 answer
Omework Assignment Question 4 of 5 - /1.5 E Assets Liabilities Accts. Rec Acc. Depr- •...
omework Assignment Question 4 of 5 - /1.5 E Assets Liabilities Accts. Rec Acc. Depr- • Equip- 0 + Prepd. Insur. 750 Cash 15,330 + + Supplies + 2.750 + Equip 4,760 Notes Pay. 4,760 Accts. Pay. 2.300 Int Unearned + Pay. Serv. Rev. 0 1.720 Bal. 0 Assume the following adjustment data. 1. 2. 3. 4 Su...
5 answers
1) Find the volume of 28 g CO2 at STP?a) Using your answer in #1, determine the density ofcarbon dioxide. please write clearly, thank you!
1) Find the volume of 28 g CO2 at STP? a) Using your answer in #1, determine the density of carbon dioxide. please write clearly, thank you!...
5 answers
562 95G0 5 8 2 of a QUESTION of these 8 38 solution diluted to volume of '7000 What is the final concentration?
562 95G0 5 8 2 of a QUESTION of these 8 38 solution diluted to volume of '7000 What is the final concentration?...
1 answer
Question 10 Set up the definite integral and evaluate the definite integral to determine the area...
Question 10 Set up the definite integral and evaluate the definite integral to determine the area of the shaded region. Show all work and provide your response in the box below. The curve is given by f(x)= x3 + 2x2 - 5x+3. If you cannot view the image below, please click on this link. HHHHHH HHHHHHH...
1 answer
Help with my homework question! 29)Draw out the wedge structure for the two molecules listed below:...
Help with my homework question! 29)Draw out the wedge structure for the two molecules listed below: (S)-2-methyl-3-hexanol, and (1S,3R)-3-methyl-1-cyclopentanol...
1 answer
A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?
A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?...
1 answer
Describe a scenario where someone had a birth defect, what could have been done to help...
describe a scenario where someone had a birth defect, what could have been done to help them, by the government, the community, and international organizations?...
5 answers
Complete parts a–c for each quadratic equation.a. Find the value of the discriminant.b. Describe the number and type of roots.c. Find the exact solutions by using the Quadratic Formula.$x^{2}+4 x+3=4$
Complete parts a–c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula. $x^{2}+4 x+3=4$...
1 answer
Cash is as important as profit in a company because: Managing cash improves profitability Cash is...
Cash is as important as profit in a company because: Managing cash improves profitability Cash is one of the key measures on the income statement Cash is what keeps a company running from day to day Cash is a measure of shareholder value A company has more cash today when: Customers pay their ...
1 answer
Complete the table below. Round each of your entries to 2 significant digits. You may assume...
Complete the table below. Round each of your entries to 2 significant digits. You may assume the temperature is 25 °C. conjugate acid conjugate base formula ka formula Ky x 6 ? HNO, 4.5 x 10 C,H,ONH 2.1 x 10 H,CO; 4.5 x 10-7 Complete the table below. Round each of your entries to 2 significant d...
5 answers
If the wavelength of the D sodium line in vacuum i$ 589.0 nm (speed of light in vacuum 3X10 nVs) The wavelength of light In solution having refractive index 143Select one: a.412 nmb, 2.1X10 nm5.09X1Q nm0.314 nm
If the wavelength of the D sodium line in vacuum i$ 589.0 nm (speed of light in vacuum 3X10 nVs) The wavelength of light In solution having refractive index 143 Select one: a.412 nm b, 2.1X10 nm 5.09X1Q nm 0.314 nm...
1 answer
How do you find the derivative of #e^(2x)# using the product rule?
How do you find the derivative of #e^(2x)# using the product rule?...
1 answer
Problem 3 (1 point) Suppose that a body undergoes some motion. To track this motion, we...
Problem 3 (1 point) Suppose that a body undergoes some motion. To track this motion, we mark three initial points and track where they are at some later point in time. If the initial marker points are given by the position vectors, 0 0 and at a later time point, the position vectors for these points...
1 answer
4. A 2.86 g sample containing both Fe and V was dissolved under certain conditions and diluted to 200.00 mL. Fe2 and VO ions. The titration of this solution required 22.64 mL of0.1000 M Ce" t...
4. A 2.86 g sample containing both Fe and V was dissolved under certain conditions and diluted to 200.00 mL. Fe2 and VO ions. The titration of this solution required 22.64 mL of0.1000 M Ce" to reach end point. A second 50.00 mL aliquot was passed through a Jones reductor to forn ions. The titrat...
1 answer
Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon’s customers...
Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilon’s customers make reservations through Epsilon’s website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle thes...
5 answers
[10 points] Find the complete solution to the system
[10 points] Find the complete solution to the system...
1 answer
How is self-care related to self-leadership?
How is self-care related to self-leadership?...
1 answer
Part A What is the magnitude of the net force exerted by the other two charges...
Part A What is the magnitude of the net force exerted by the other two charges on charge 20nC? Express your answer using two significant figures. Three point charges are located on the positive x-axis of a coordinate system Charge q 20 nC is 2.0 em from the origin, charge -2.0 nC is 4.0 crm from the...
5 answers
Unielntutefunelmumaraptnktonilng Jn boleaneeiclyid In 400 Jelocnet Mumnyi Wtaue Iori 44le 0l Orenutee Ale) , Ue natint 6thc tatteol trne 6, 4 Uea concorki oami 0 5k In Iha Illew # uwlatk and Oion by (n(n Tanlanllun(u4} Ib/0"caaaa [aLuliyto [ul EJro?i Q[ eulnInle7aUeehniemaneto
Unielntutefunelmumara ptnktonilng Jn boleaneeiclyid In 400 Jelocnet Mumnyi Wtaue Iori 44le 0l Orenutee Ale) , Ue natint 6thc tatteol trne 6, 4 Uea concorki oami 0 5k In Iha Illew # uwlatk and Oion by (n(n Tanlanll un(u4} Ib/0" caaaa [a Luliyto [ul EJro?i Q[ euln Inle7a Ueehniemaneto...
1 answer
Chemton Question 16 of 16 How many moles of calcium atoms do you have if you...
Chemton Question 16 of 16 How many moles of calcium atoms do you have if you have 5.15 x 1021 atoms of calcium. (The mass of one mole of calcium is 40.08 g.) mol c +/ 0 x 100...
1 answer
A rocket cruising past earth at $0.800 c$ shoots a bullet out the back door, opposite the rocket's motion, at $0.900 \mathrm{c}$ relative to the rocket. What is the bullet's speed relative to the earth?
A rocket cruising past earth at $0.800 c$ shoots a bullet out the back door, opposite the rocket's motion, at $0.900 \mathrm{c}$ relative to the rocket. What is the bullet's speed relative to the earth?...
1 answer
What information does this trend chart provide? (IMAGE DESCRIPTION: Sample chart showing monthly management reserve (MR)...
What information does this trend chart provide? (IMAGE DESCRIPTION: Sample chart showing monthly management reserve (MR) usage, cost variance (CV), and schedule variance (SV) from May 14 through September 14. Approximate MR values are: May 2.2, June 2.1, July 1.5, August 1.3, September 1.2. Approxim...
5 answers
Sin n)' 10- Determine whether the series converges Or diverges: n(n+3)
sin n)' 10- Determine whether the series converges Or diverges: n(n+3)...
5 answers
List some advantages and disadvantages of an experimental study.
List some advantages and disadvantages of an experimental study....
5 answers
Find the maximum rate of change of the function f(x, Y, 2) = xy + Yz xz at the point Po(3, -1, 4)Find the unit vector direction in which the greatest rate of change occurs (Your instructors prefer angle bracket notationfor vectors_
Find the maximum rate of change of the function f(x, Y, 2) = xy + Yz xz at the point Po(3, -1, 4) Find the unit vector direction in which the greatest rate of change occurs (Your instructors prefer angle bracket notation for vectors_...
1 answer
What is the mass of 4.86 x 10^21 molecules of ethanol, C2H5OH?
what is the mass of 4.86 x 10^21 molecules of ethanol, C2H5OH?...
1 answer
Accounting Question
Please Help the below question:Question 3(a) Tobaco Berhad, with the Ringgit Malaysia as its functional currency, purchases plant from a foreign entity for $18 million on 31 May 2019 when the exchange rate was $2 to RM1. The entity also sells goods to a foreign customer for $10.5million on 30 Septem...
1 answer
You must perform an ECG on this patient. Describe the steps in the procedure.
you must perform an ECG on this patient. Describe the steps in the procedure....
1 answer
(II) $(a)$ Can the reaction $p+\frac{7}{3} \mathrm{Li} \rightarrow \frac{4}{2} \mathrm{He}+\alpha$ occur if the incident proton has kinetic energy $=2500 \mathrm{keV} ?(b)$ If so, what is the total kinetic energy of the products?
(II) $(a)$ Can the reaction $p+\frac{7}{3} \mathrm{Li} \rightarrow \frac{4}{2} \mathrm{He}+\alpha$ occur if the incident proton has kinetic energy $=2500 \mathrm{keV} ?(b)$ If so, what is the total kinetic energy of the products?...
5 answers
Find and classify all critical points of f(x, Y) = Yx y-i-Zv_ 36y 16. (Order vour answers from smallest to largest x, then from smallest to largest y.)critical pointsclassification(x,Y)Sclect ClassificationXY)Selec Classification(x,Y)Select Classification(y)Select Classification
Find and classify all critical points of f(x, Y) = Yx y-i-Zv_ 36y 16. (Order vour answers from smallest to largest x, then from smallest to largest y.) critical points classification (x,Y) Sclect Classification XY) Selec Classification (x,Y) Select Classification (y) Select Classification...

-- 0.028416--