5

QuestionThe average repair cost of & Qicrowave Ovel IS 55S. With & standard deviation of 85 The costs are nonally distributed If [2 ovens are repaired fi...

Question

QuestionThe average repair cost of & Qicrowave Ovel IS 55S. With & standard deviation of 85 The costs are nonally distributed If [2 ovens are repaired find the probability that the mean of the repair bills will be greater than 6050 0.0150 None of these0 0.10560 0.0062

Question The average repair cost of & Qicrowave Ovel IS 55S. With & standard deviation of 85 The costs are nonally distributed If [2 ovens are repaired find the probability that the mean of the repair bills will be greater than 605 0 0.015 0 None of these 0 0.1056 0 0.0062



Answers

Repairs The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.
$$\begin{array}{|c|c|c|c|c|}\hline{\text { Repair Calls }} & {0} & {1} & {2} & {3} \\ \hline \text { Probability } & {0.1} & {0.3} & {0.4} & {0.2}\\ \hline \end{array}$$
a) How many calls should the shop expect per hour?
b) What is the standard deviation?

So we're given a normal distribution for the, uh, repair cost of the car, which is always a pain. But you have to deal with it. And $367. I'm surprised that's the average cost. And there's our standard deviation. And we are told to assume that this is normally distributed and we want to find the likelihood that a cost is higher than $450 which means we $450. You know, we could go through and Mark, if I take the 3 67 and add on 88 that comes out to be $455. So this is 4 55 right here, one standard deviation away. So you're almost one standard deviation. You're finding that area right now, so we need to convert that to a Z value. And remember, we take what we got minus the main and then divided by the standard deviation. And that gives us a Z value of 4 50 minus 3 67 divided by 88. And again, I know that because it's just a little less than one from my picture. We get that that Z value is 10.9432 roughly. And then you can either use your table in the book, which means you only use this or you can use your normal CDF button. I'm going to use my normal CDF, but I don't have to have my book right here, so and I can put in second answer for the lower limit. So I'm putting in this Z score and then up to a big number for my upper. I'm going to put in 1000 and then I'm gonna leave the mean at zero and the standard deviation at one. And when I get that, I get the probabilities 0.17 basically 31728 So it's about a 17% chance of that happening. And then part be asked us to find What's the likelihood that the cost will be less than 2 50 and again to 50 is going to be down here someplace. So you know, it's a negative z value and let's find out what it is. 2 50 minus the mean divided by the standard deviation, and you can actually go back up to the my calculation and just retyped that 2 50 place of that and we get that that Z value. Is this the value of negative 1.3? Roughly 33? It's like 3295 So I'll say that. And again, I'm going to use my normal CDF button. So second and distribution normal CDF. But now I use the lower limit is like negative negative 1000, and then it's going up to a value of that. Second answer that negative 1.33 and and I get less than 10% 100.918 So about a 9% chance of that happening, then Part C. We want to find what's the likelihood that your car repair will be between 2 50 and I don't remember if it says inclusive. But regardless of whether it does or not, we would. Your answer is going to be the same if we include the endpoint or not include the endpoint. And luckily for us, we already know the Z values. This Z value is negative 1.33 from the previous question and this Z value let's find it is 0.9432 and so I'm definitely going to use my normal CDF button for that and my normal CDF. I can put in the negative 1.33 as the lower limit and then this 0.9432 for the upper limit and leave the mean and standard deviation at one, and I find out that that probability is 10.735 So about a 73 74% chance of that happening now the final question is, we're going to have to do it in reverse order. We want the value that is the lowest 5% if you know the cost of repair is in the lowest 5% that means we want this area down here to be 0.5, and we need to find what that Z value is. That corresponds with that which you can use your inverse normal button and put the area as Point Oh five leave the main at zero and a standard deviation at one, and I find out that this value is negative 1.645 and that's the Z value, and then we need to convert it. So negative 1.645 is equal to the score, Um, looking for I call him that. Acts minus the mean, which is 3 67 kind of for God, divided by 88. And so, if I take that negative 1.645 times the 88 add on 3 67 I find out that that score is $222 in, like, 24 cents, so roughly 200 $22. So that would be anything that and lower would be in the lower 5%.

In this problem. We have a population of 800 homes and the average value of the home is $82,000 with a standard deviation of $5000 from that population. We're going to select a sample and the sample size is 50. Because we're saying if 50 homes are for sale, we want to find the probability that the mean is greater than 83,500. So because we selected a sample size that was large enough, no matter what shape the distribution of the population is, the sample distribution will be bell shaped or normal. Because we're dealing with a sample, we need to find the average of the sample means and we need to find the standard deviation of the sample means otherwise known as this um, standard error of the mean to find the average of the sample means the central limit theorem tells us it will be equivalent to the average of the population, and in this case it will be 82,000. The standard deviation of sample means, according to the central limit theorem, will be the standard deviation of the population divided by the square root off the sample size. So in this case, it will be 5000 over the square root of 50. So on our bell curve, we're going to start by putting the average the 82,000 in the center and we will need to calculate Z scores. So in this particular problem, we're talking about having a value of 83,500 and actually greater than that. And in order to find our Z score, we're going to have to apply the formula for using samples as X bar minus, um, use of Expo are divided by Cygnus X bar. So we need thes e score for 83,500. So we're going to say Z equals 83,500 minus 82,000, divided by 5000 divided by the square root of 50. And we do that. Our Z score turns out to be 2.12 so we can put a 2.12 up here. So when we're talking about the probability that the average of the 50 homes, um is greater than 83 5, we can also say that's the same as the probability that the Z score is greater than 2.12 and that's the same thing is saying one minus. The probability that the Z score is less than 2.12 were one minus 0.9830 and we got that 0.9830 by looking in the standard normal table in the back of your book, and the overall probability would be 0.170 So just to recap the probability of the 50 homes that are for sale in this a certain area having a valley an average value greater than 83,500 would be 0.170

38. The amount of money spent weekly on cleaning, maintenance and repairs at a large restaurant was observed over a long period of time to be approximately normal. What the mean of $615? With the standard deviation $42? Yeah, am if 646 is budgeted for next week, what is the probability that the actual cost will exceed the budgeted amount? So the probability X will exceed 646? So we're gonna say that X is approximately normal. Draw the curve to get an idea of what's going on here. 6 15 is our centers are mean, our center deviation is 42 so I want to space this out 42 when he said, so we're gonna add 42 to that and we get 6 57 and then there's also a 2nd 3rd center deviation, there's no need to put one standard deviation below 6 15 puts us up 5 73 and I want to know what's the probability that I'm exceeding 6 46. So, somewhere in this range here, So, so I'm looking for the area to the right of 6 46 so we can use our tia 83 or 84 calculator and use the normal CDF command here, we have to insert what are lower bound. Is this essentially where we're starting our shading, which is at 6 46. Our upper bound is where we stop shedding. Technically that's never because it goes to infinity, so we're going to put in and and then just a series of nance to indicate a large number, I mean is 6 15 standard deviation here is 42. We can plug this in and we get zero point 23 B. How much should the how much should be budgeted for weekly repairs, cleaning the maintenance, so that the probability that the budget budgeted amount will be exceeded in a given week is only 10%. So what I'm looking for here is some amount of use it, read some amount so that if they go over there is only a 10% chance of going over. So I want to use my inverse norm command this time in my T 84 calculator. Um The 84 calculators are really geared to be left sided. Um A newer version will give you a choice between left, middle or right, but we're gonna focus on the left side of the version of this. So the area to the left of this red line again area to the left is 90%. So 900.90 with our mean of 6 15 and our center deviation of 42. That gives us a budgeted amount of $668.83. Now, if you have a more up to date version of the T i 84 calculator, um, you could put in 840.1 as your area, as long as you have the feature, uh to select the right sided shade.

You know this problem? We are told that on average 20% of toasters require repairs within one year. So this means r. p. value is going to be 0.0. Mhm. Now 20 toasters are randomly selected and so this means that are in value this morning. So using a binomial distribution of the probability of that is April, two, x. Times .20 to the X. Times .80 To the 20-1. Thank you. Now first we want to find the probability that at least accept them will require repairs is less than .5 and so on. And we want to find the probability that at least acts wax is greater than relax is less Than 0.5. And what this means is that we want the some for Mexico's from X to 20 of 20 choose acts Times .20 to the X. Times .80 to the 20 -X. To be less than or equal to 0.5. And so all we're doing here is adding up all the probabilities from X to 20. And we want this to be less than or equal 2.5. I'm just gonna get some checker. We know this number should be less than 20. Let's try 15 and see what it gives us here on this left hand side. And so they're 20, choose X Times .22. The X. I was .8 to the 20-1. And well some this from 15 to 20 and see what that gives us doing. That gives us 1.8 Times 10 to the -7. And so that is way too small. Way too small. Now let's try in is 10 then and see what that gives us Now. 15 does is less than .5 but we want the smallest possible number could be so let's write 10 10.0025. And so that's still less than any for the .5. But we can get even smaller. And so let's try in six maybe Toward a some from 6 to 20. I'm sorry not in a sense that should be absent Access Access 10 Access 15. Uh huh. When I was six this is .1957. Still less than .5 but we can get even smaller. Try maybe three. So let's find some from 3 to 20. Now that's .79. And so that's too big. It's between three and 6. Let's try five. See if I've still works. You know that six does let's make it one smaller, notified. It gives us .37. And so let's drive 44 words and four is the smallest If four doesn't work than five is the smallest Ford gives us .59. And so that's too big. And so X. Is five. So the probability that five or more Have the effects is still less than .5 which is five. Mhm. No indeed. We want the probability that at least one of them will not require repairs. Yeah. And so we want the probability now if at least why of them will not require repairs. Mm. This means we're looking at from the parasites. We want Y is greater than or equal to Y. So it will be the sum from why is why to 20 of 20 choose why Times .8 to the wind notice I flipped it here because we wanted to not require repair. We want this to be greater than we put 2.8. Uh huh. And so now let's guess and check off of this. It's going to take the some Of 22 is why I was .8 to the Y. 1.2 to the 20 -Y. And let's try from 3 to 20 year. Let's let's try y. equals three. Why it was 3.999. And so that's That is bigger than .8. Well let's try Higher number here. Let's try. Why is 6? And so let's find the sum from 6 to 20 And still .999. Mhm. So let's try. Why is 11 maybe? And I'm just guessing and checking it. This is still .99. That's maybe why is 15? Why is 15 gives us .804 which is still bigger but just barely. And so why is 15 will be the largest number possible? Yeah.


Similar Solved Questions

4 answers
Al+2ulo: p 100+ + 312 1z - (2) n 1+ 3/2 Hzo? 121l2 23 + 5/2 Hz ~ (3) /b A / 10 #kt 4bat SamTle *1 $ approx &0- 952/2To check the answer of Al from che graph above; calculate the % Alby lsing' Eqwation from the introduction scction of the lab and the NH; calculated front question
Al+2ulo: p 100+ + 312 1z - (2) n 1+ 3/2 Hzo? 121l2 23 + 5/2 Hz ~ (3) /b A / 10 #kt 4bat SamTle *1 $ approx &0- 952/2 To check the answer of Al from che graph above; calculate the % Alby lsing' Eqwation from the introduction scction of the lab and the NH; calculated front question...
4 answers
Evaluate the line integral Fadr where € is the counterclockwise path on the unit circle starting and ending at (0,-1) and F(;y) = 2yi+4xj. You may use any method YOu choose t0 evaluate this line integral, but show all your work:
Evaluate the line integral Fadr where € is the counterclockwise path on the unit circle starting and ending at (0,-1) and F(;y) = 2yi+4xj. You may use any method YOu choose t0 evaluate this line integral, but show all your work:...
5 answers
To conclude that thehaincreased decreased not changed9 of 10 ID: MST.HT.TM.05.0010[3 points]
to conclude that the ha increased decreased not changed 9 of 10 ID: MST.HT.TM.05.0010 [3 points]...
5 answers
About point in 2D forceCompute the moment about pointS0O Ncross out the right answerM-720M-632M-680 M-530[Nm]JEnf
about point in 2D force Compute the moment about point S0O N cross out the right answer M-720 M-632 M-680 M-530 [Nm] JEnf...
5 answers
3 5 9-3 Vz = 2pt) Let V1and V3Let28 9 16WFind the coordinates of W with respect to the (ordered) basis {V1, V2. V3}. In other words, find the values /, $,t € R such that w = rV + SV2 + tva
3 5 9 -3 Vz = 2 pt) Let V1 and V3 Let 28 9 16 W Find the coordinates of W with respect to the (ordered) basis {V1, V2. V3}. In other words, find the values /, $,t € R such that w = rV + SV2 + tva...
5 answers
What is the product of the following reaction? HBrOAB)
What is the product of the following reaction? HBr OA B)...
2 answers
Exzmple 14.11 Define e+y_ +2 for (x, Y, 2) in R' ftx, y 2) = sin(ryz) + second-order derivatives shows that at the point (0, 0, 0), short computationvf(, 0, 0)The following theorem explains how the Hessian matrix enters into second: derivative cakculations of the sections of a function of several variables.
Exzmple 14.11 Define e+y_ +2 for (x, Y, 2) in R' ftx, y 2) = sin(ryz) + second-order derivatives shows that at the point (0, 0, 0), short computation vf(, 0, 0) The following theorem explains how the Hessian matrix enters into second: derivative cakculations of the sections of a function of...
5 answers
Here t0 103 =500 mm; inlet Question a and 000 mm; shown gage pressures 3 diverts are watei =100 kPa; and through 3 respectively. angle 1800. Determine The the diameter following asing ( teledata M inlel (SG-1, 2 % 16 1 the elbow outlel. TheThe H at the (x direction) exit componer2 5;15. 2,16.0,16.8,17.6)(-39270;-41 233;
here t0 1 03 =500 mm; inlet Question a and 000 mm; shown gage pressures 3 diverts are watei =100 kPa; and through 3 respectively. angle 1800. Determine The the diameter following asing ( teledata M inlel (SG-1, 2 % 16 1 the elbow outlel. The The H at the (x direction) exit componer 2 5;15. 2,16.0,16...
5 answers
1d [Jd [submit AnswerTry Another Versionemtaining sidwaullJd [(2) The element with an clectron configuration period pOE of 1522,22p' js in group clectron configuration (1) The element with an and period of 1s22s22p"3s23p"4s23d? is in groupMe 78tor (bIs question_ Dipzur
1d [ Jd [ submit Answer Try Another Version emtaining sidwaull Jd [ (2) The element with an clectron configuration period pOE of 1522,22p' js in group clectron configuration (1) The element with an and period of 1s22s22p"3s23p"4s23d? is in group Me 78 tor (bIs question_ Dipzur...
5 answers
Part €How large is the image of the Sun on film used in a camera with a 125-mm-focal-length lens? Express your answer using two significant figures and include the appropriate units.pAIhiValueUnitsSubmitRequest AnswerPart DIf the 55-mm lens is considered normal for this camera, what relative magnification does each of the other two lenses provide? Express your answers using two significant figures separated by a comma:AZdMz6 [ relalive M125 TII relative
Part € How large is the image of the Sun on film used in a camera with a 125-mm-focal-length lens? Express your answer using two significant figures and include the appropriate units. pA Ihi Value Units Submit Request Answer Part D If the 55-mm lens is considered normal for this camera, what r...
5 answers
Question 5 Marks): Frove. using the formal definition; that limz_,s(2)'/8 = 2.Question 7 (5 Marks): Prove; using (uc formal delinition, (hat lit , '1= VI-IQuestion 8 5 Marks):Prove, using the formal definition; that lim, _(40"+00
Question 5 Marks): Frove. using the formal definition; that limz_,s(2)'/8 = 2. Question 7 (5 Marks): Prove; using (uc formal delinition, (hat lit , '1= VI-I Question 8 5 Marks): Prove, using the formal definition; that lim, _ (40" +00...
5 answers
Let & =4)-(E)-() and & = 05 Is din Span{a,b,c}? Why why not?
Let & = 4)-(E)-() and & = 05 Is din Span{a,b,c}? Why why not?...
5 answers
The following series converges because it is a p-series withp=3. Use the Integral test to prove it.n=1∞1n3
The following series converges because it is a p-series with p=3. Use the Integral test to prove it. n=1∞1n3...
5 answers
The figure below shows an object of mass m-3.3 kg which is connected t0 a string of length r-0.95m, When the object is at the bottom of the circle it has velocity Vb =10.1 m/s What is the tension in the string at the top of the circle?Select one: 192.7 [email protected] N
The figure below shows an object of mass m-3.3 kg which is connected t0 a string of length r-0.95m, When the object is at the bottom of the circle it has velocity Vb =10.1 m/s What is the tension in the string at the top of the circle? Select one: 192.7 N 144.5N 115.6N 385.3 [email protected] N...
5 answers
Let xG] Fi a matrix A Sucn Etab F(x) = 6x*+81,'+4k5*_ 2X % ~Gxk-xAx, H) Verfy tht 2f JX =2AX.
Let xG] Fi a matrix A Sucn Etab F(x) = 6x*+81,'+4k5*_ 2X % ~Gxk-xAx, H) Verfy tht 2f JX =2AX....
4 answers
2 J23J2b#35TS48TS#5 ISv7ule~u EennPie [794/3#IcUS795_Lia#/47L9v'1)
2 J 2 3J2 b# 35 TS 48 TS #5 ISv 7ule ~u Eenn Pie [ 79 4/3 #Ic US 79 5_ Lia #/4 7L 9v '1)...

-- 0.020521--