5

An airliner carries 300 passengers and has doors with a heightof 72 in. Heights of men are normally distributed with a mean of69.0 in and a standard deviation of 2....

Question

An airliner carries 300 passengers and has doors with a heightof 72 in. Heights of men are normally distributed with a mean of69.0 in and a standard deviation of 2.8in. Complete parts (a)through (d).a. If a male passenger is randomly selected, find theprobability that he can fit through the doorway withoutbending.

An airliner carries 300 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.



Answers

Doorway Height The Boeing $757-200$ ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. (based on Data Set 1 "Body Data" in Appendix B). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. b. If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72 in. c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? d. When considering the comfort and safety of passengers, why are women ignored in this case?

Okay, So for this problem, we were told that, dear. According to the health survey, the Iight the height of adult males in the United States are normally distributed was mean of 69. It's not inches and 28 inches. So so we're given mean, so mean We don't use a good meal because 69 inches and then you given the this standard deviation. It's 28 sanitation where you would use sigma because 2.8 inches. So that's how you define. So so the survey is normally be modeled. Relax. Is it because 21 over and in the square to pi times sigma time Miss E to the minus 1/2 X minus mu. It was Sigma squared. And this is true for all ex. This is true for all ex great, and you questions you so that means effort max zero. Every else in that domain you can plug in Miracle 69 and Sigma equals 2.8 inches to this expression here. Now the question would like. The answer is to determine the probability that an adult male shoot at random chosen a random will be between 65 inches and similar three inches tall. Hey, it's similar to say What is P? Alexe is between, uh, 65 and 73 inches tall. So, mathematically, this is you. We can translate this into a little trouble. We will become so limits of integration are gonna be from 65. Consider it. It's free after lex D X. So all right. Now you can plug in old in America about stuff after we see the ready. So mu is 69 signals to plate into f of X. Now, for our into go, um, interval will become one over to two pi and then square root every signal. What is Cigna Signature stamp? Civilian. We used to Quinn eight inches e to the minus 1/2 in the X minus 69 of a sigma, which is 2.8. And then you square the entire thing. The X So that's the interval we need to evaluate. And now limits are from 65 two 73. Is the car into a goal we're supposed to do? You should see that I pushed out this constant fear. One over to Red Troop I, Thomas 2.8. Because of that Constance, I pushes how it automatically So the only part of integral you have to do is this part here, and news board is no elemental way to do it. Um, you can use but war from which is freely available on the Web. Or you can use my people. The people are going to uh, So anyway, So if you put this into an integral calculator, uh oh, are integrating numerically for them. We're using that Simpson's rule. You will get something like 0.8469 And so or roughly roughly rather the 85% 85% now moving on to part B. So before B, we would like to know the percentage of the off the adult male population that is more than six feet six feet. Remember, You know, the units were using the interest, so we needed to hurt six feet. So how many in deciding six feet so six feet. He's in close to 12 every six inches because one foot one foot it was 12 inches. So you might plan six by 12. You get 72 senator two inches. Um, so now that so the question becomes, what is the probability was a problem. X rated integrity, too. On translating this integral, it will be Seamus integrating from 72 to infinity of f of x d x. When we put in everything you should get inta go. And he's going to be the constants that before So one of a square to pie Time of sigma, which was 2.8 and then the inter go from 72 to infinity. Then you have ye to the miners 1/2 x minus 6.69 point zero of a 2.8. Okay, then the whole thing squared dx again. This integral has no elemental form. This is how you do the interval. Now there are trucks of doing intervals like that spirit. I'm not gonna go into that. Um so using Wolfram maple or what about Integral Cog? Yeah. If you should get something like zero point 14 or 14%. 14% questions asking for an answer in percentage to. So you get 14%. And that's how you have that question

So in this question, we're told the height of adult men are normally distributed mean of 69.1". Standard Division 2.92". and one requirement is that men must stand between 60 and 80 inches tall, so frank property that randomly elected man meet the height requirement for military service. That's a probability. The disease between 3.73 And -3.12. So that's basically .9999 -1009, which gives us .999. What this probability Part. Beevers told that 23 men contact a recruiter. They're all independent. Find the quality that all of them meet hide requirements. So that's just .999 to the power of 23 Which is .9773.

So the first thing we want to do is solve the probability the X is going to be less than 66. So we need our Z score for 66 which is given by the equation above. So you take 66. We have 66 minus mu, which is the, um, population, Uh, mean, which is 69.4 and then we divided by our standard deviation of 2.9. Yeah, from this gives us a Z score of negative 1.17 So then, to get our probability, we just used RZ table and see that the probability that are Z score would be less than negative. 1.17 is 0.1 to 1. And that's the answer to part A on part B. We're actually going to do part C before we do part beat. So part C part C is the probability. Alright, I'll switch colors Probability that X is greater than 72. Oh, so now we need our Z score for 72 which we calculate the same ways before, except now, instead of using 66 we're going to use 72 to use that same equation on, we get our new Z score of 0.897 Now, we can use this the same way that we used the last one to find the area under the curve to the left of the sea score. And that will tell us the probability that X is less than 72. But we actually want greater than so. In order to do that, we just need to do one minus that value. So again, we're going to do one minus our value that appears on RZ table 4.897 and that value is 0.815 the one minus 10.815 This gives us the area to the right of rz score, which again is giving us X greater than 72. The answer is 0.185 So that's our answer to part C. Now we can go back and do part B. A Part B is the probability the X is between these two values, so it's going to be greater than 62 or less than 72. So this we're going to be using both of disease scores. We used previously our standard normal curve look something like this. So we have our two Z scores, which would be something like here and here. One more to the left is going to be our negative 1.17 Yeah, mhm. And then our second z score of 0.897 would be to the right. All right. So before we calculated the area to the left of our first D score, which is this area and then we used we were looking for the area to the right 5.897 We did. In order to do that, we subtracted the area to the left, which again we solved to be 0.815 So this green area was the 0.815 and the red was the 0.1 to 1. So now, to get this area just in between those two, this area, we just need to subtract the 0.1 to 1 from our 0.815 So me dio 0.815 which is the whole area to the left of our second Z score, which is telling us the Probability X is less than 72. We're subtracting probability that it's less than 62. 0, I'm sorry. I wrote 62 in here, and it's supposed to be 66. So 0.815 minus the 0.1 to 1 from above on. Then once we subtract thes, you should get an answer of 0.694 you know. So that's our answer to Part C. And then finally, Part D. We're just looking for unusual values that we might find. And that would be anything that's outside of three Standard deviations of our mean again are mean is the 69.4 that would be 69.4 plus or minus three times our standard deviation, which was 2.9. So unusual values would be anything that is less than 60.7, and that's 69.4 minus three times 2.9. So if X was less than this, or if X was greater than 69.4 plus three times the standard deviation, which gives us 78.1, those would both be very unusual occurrences. That's our answer to party

With them, you Equal to 69 and A sigma equal to 2.8. We have the probability have 65 between 65 and 73. to be called to Dante Girl From 65 to 73 One divided by 2.8 square roots of to buy. Then we have exponential to You have -1 -69 to the power to divided by two times 2.8 squared or D eighth. So using a calculator, this is approximately zero points AIDS for serving. So this is the probability that's the months of iron. The probability that the adults mutual scene At a random is between 65 and seven ctv inches. Then for the second part b The percentage of the adults made population we are seeing is more than six ft. So so we have the publicity That it is more than six ft. It's going to be equal to the probability that it is more than 72 and this is equal to one minus so 1- The Probability. So the interval from 0 to 72, which is approximately 1 0 points, is five. It's and this is equal to zero points 142. So this implies that you have 14.2, His Saints, 40.2 of the adults. Uh, that's meal population population is more than six feeds, so.


Similar Solved Questions

5 answers
18. lim T - X = 1 X+T sin x
18. lim T - X = 1 X+T sin x...
5 answers
A 39.5 mA current is carried by uniformly wound air-core solenoid with 425 turns a 15.0 mm diameter; and 10.0 cm length_ (a) Compute the magnetic field inside the solenoid.Compute the magnetic flux through each turn_ T-m2(c) Compute the inductance of the solenoid. mH Which of these quantities depends on the current? (Select all that apply:) magnetic field inside the solenoid magnetic flux through each turn inductance of the solenoid
A 39.5 mA current is carried by uniformly wound air-core solenoid with 425 turns a 15.0 mm diameter; and 10.0 cm length_ (a) Compute the magnetic field inside the solenoid. Compute the magnetic flux through each turn_ T-m2 (c) Compute the inductance of the solenoid. mH Which of these quantities depe...
5 answers
QUESTION 5Is the set of vectors of the form:2a -b - 1 X = 3a + b - 1 where a and b are real numbers, a subspace of R3 ? 4b - 1YesNo
QUESTION 5 Is the set of vectors of the form: 2a -b - 1 X = 3a + b - 1 where a and b are real numbers, a subspace of R3 ? 4b - 1 Yes No...
1 answers
Solve the Laplace equation Uzs + Uyy =0 for tle mesh r = 0=4. T= 1=4 given that "(O.y) U.u(i.0) = O.u(l.y) = 1OU.u(i.1) 1UU ad h = 1/3 aud k = 1/2
Solve the Laplace equation Uzs + Uyy =0 for tle mesh r = 0=4. T= 1=4 given that "(O.y) U.u(i.0) = O.u(l.y) = 1OU.u(i.1) 1UU ad h = 1/3 aud k = 1/2...
5 answers
Lines 30 and AB inlersect al point C8 8 & 6 What Is the 1
Lines 30 and AB inlersect al point C 8 8 & 6 What Is the 1...
5 answers
For the following electrochemical cellSn(s)lSn2-(ag, 0.0155 M)IIAg (aq; 2.50 M)IAg(s)wrile lhe nel cell equalion. Phases are oplional. Do not include the concentrationsSn(s) + 2Agt(aq)Sn" + (aq) + 2Ags)Calculate the following values at 25_ C using standard potentials as needed_NumberNumbermo [NumderNumberGrxnmol
For the following electrochemical cell Sn(s)lSn2-(ag, 0.0155 M)IIAg (aq; 2.50 M)IAg(s) wrile lhe nel cell equalion. Phases are oplional. Do not include the concentrations Sn(s) + 2Agt(aq) Sn" + (aq) + 2Ags) Calculate the following values at 25_ C using standard potentials as needed_ Number Numb...
5 answers
LL _ A Op Students Ccected Jighschcol n tct Sucve y Gostet 470867 howsucwad many boucs da uou Etuly #e Eirst 60 Students_who Jcok Kec? ansuerea into Teadercg obleratg? sumpe T0 0 Arph . wlat @pplea 1 CnJen jene 4 5 3 3 1O 50 2 H t BO 3 7 ; 8 5 L 1 4 18 4 05 (c € Fo70
LL _ A Op Students Ccected Jighschcol n tct Sucve y Gostet 470867 howsucwad many boucs da uou Etuly #e Eirst 60 Students_who Jcok Kec? ansuerea into Teadercg obleratg? sumpe T0 0 Arph . wlat @pplea 1 CnJen jene 4 5 3 3 1O 50 2 H t BO 3 7 ; 8 5 L 1 4 18 4 05 (c € Fo70...
5 answers
LecTLre $ exawple 5 tre !em 44e4 air tuvsixe scev Pawsicy Pz = I50 Ibl/ * ayster = Itbo'R Pz = /4.8 16f44+ Ki Get dwcv T,= Y6o'1 iba_ E0 =i.o Abh 8c ict= 65640 RIL ct Kr: Grd Wot Lhp) avscheticx$ /cetal - v= Cerom 644+84 5 Kehe Wzh 3m9 shtc M _Flzpe-. syleshe ~ake (6#t AvAvL Spec Ket+ {jaai 545
LecTLre $ exawple 5 tre !em 44e4 air tuvsixe scev Pawsicy Pz = I50 Ibl/ * ayster = Itbo'R Pz = /4.8 16f44+ Ki Get dwcv T,= Y6o'1 iba_ E0 =i.o Abh 8c ict= 65640 RIL ct Kr: Grd Wot Lhp) avscheticx$ /cetal - v= Cerom 644+84 5 Kehe Wzh 3m9 shtc M _Flzpe-. syleshe ~ake (6#t AvAvL Spec Ket+ {j...
5 answers
Exercise Emhc"[ is dcfiucl {13679,1}. W three sulstts #S A = {135 B = {9M} C 39} A-SIe that cch element has prolbility 1/6. Findl th following prolubilitiex: (#) PPIA]; (W) PIBI; (c) PIC], (d) PIAU BI; () PlAuC], () PI(AIC)U BJ:
Exercise Emhc"[ is dcfiucl {13679,1}. W three sulstts #S A = {135 B = {9M} C 39} A-SIe that cch element has prolbility 1/6. Findl th following prolubilitiex: (#) PPIA]; (W) PIBI; (c) PIC], (d) PIAU BI; () PlAuC], () PI(AIC)U BJ:...
5 answers
Name several forms of indexing in the private and public sector.
Name several forms of indexing in the private and public sector....
5 answers
400)i 6 0Uj 7 (Xk NIC : with _ in meters Fiqure 23-34 lectric llux What is the net= charge = contained by the cube? Problem 10, coulomb: J) What is Figure 23-35 shows closed Gaussian surface in the shape cube of edge length 2() m; with one curel 5.0 m; 4W)m The cube lies in region where Ihe electric [ield vector 1s given by E ~Jui - 4.OOyzj J.00K NIC , with meters; Whut Is Lhe: nel charge contained by the cube?IS the nltheFigure 23-35 Problem [
400)i 6 0Uj 7 (Xk NIC : with _ in meters Fiqure 23-34 lectric llux What is the net= charge = contained by the cube? Problem 10, coulomb: J) What is Figure 23-35 shows closed Gaussian surface in the shape cube of edge length 2() m; with one curel 5.0 m; 4W)m The cube lies in region where Ihe electric...
5 answers
With partial differential equation Ut 4 Uxx and u(jAx ,nAt) or uj determine the formula to calculate u5+1 use finite difference method with a. Forward Time dan CenterSpace (FTCS) b. Center Time dan Center Space (CTCS)
With partial differential equation Ut 4 Uxx and u(jAx ,nAt) or uj determine the formula to calculate u5+1 use finite difference method with a. Forward Time dan CenterSpace (FTCS) b. Center Time dan Center Space (CTCS)...
5 answers
Define electrode, anode, and cathode.
Define electrode, anode, and cathode....
5 answers
1. (5 pts) The table below gives information about the times it took some people to read newspaper article: Construct histogram for the given data.Time,t (e) Frequency 0 <t = 2020 < t < 3030 < t < 4011040 < t <4545 < t <5050 < t < 80
1. (5 pts) The table below gives information about the times it took some people to read newspaper article: Construct histogram for the given data. Time,t (e) Frequency 0 <t = 20 20 < t < 30 30 < t < 40 110 40 < t <45 45 < t <50 50 < t < 80...
5 answers
The surface tension of dilute solutions of phenol in water at303 K are: Wt%0.0240.0470.1180.417 ϒ (N/m)0.07260.07220.07130.0665 Calculatethe surface excess concentration (Γ) for 0.100 % solution
The surface tension of dilute solutions of phenol in water at 303 K are: Wt% 0.024 0.047 0.118 0.417 ϒ (N/m) 0.0726 0.0722 0.0713 0.0665 Calculate the surface excess concentration (Γ) for 0.100 % solution...
5 answers
Which of the following sequences is strictly decreasing745} - 1=]None1{(-1)"7+2 m=]6 I_ {725} m=]
Which of the following sequences is strictly decreasing 745} - 1=] None 1 {(-1)"7+2 m=] 6 I_ {725} m=]...
5 answers
3.Find the domain of the vector functionr(t) = (t2 _ 9,In(t + 5),V81 -tz)Use traces t0 sketch and identify the surface: Identify the surface. Provide explanations: 3x2 + y +222 = 0
3.Find the domain of the vector function r(t) = (t2 _ 9,In(t + 5),V81 -tz) Use traces t0 sketch and identify the surface: Identify the surface. Provide explanations: 3x2 + y +222 = 0...
5 answers
Consider the overall reaction that occur in this experiment2H-(aq) CIO-(aq) 2S2032-(aq)Cl-(aq) S-O6-(aq) Ho()Assign oxidation numbers to all the elements in this reaction_ Which ion is oxidized? Which ion is reduced? (fcmula) (fcmula)Which ion is the reducing agent? (fcmula)
Consider the overall reaction that occur in this experiment 2H-(aq) CIO-(aq) 2S2032-(aq) Cl-(aq) S-O6-(aq) Ho() Assign oxidation numbers to all the elements in this reaction_ Which ion is oxidized? Which ion is reduced? (fcmula) (fcmula) Which ion is the reducing agent? (fcmula)...

-- 0.025058--