5

In analyzing switching between different engineering degree programs for freshman, survey data has been used to estimate the following transition matrix for the pro...

Question

In analyzing switching between different engineering degree programs for freshman, survey data has been used to estimate the following transition matrix for the probability of moving between departments each month:To DepartmentDI D2 D3From D0.8The current (month share of students for the department are S0%, 309 and 209 for departments DI,D2_ and D3 respectively _What will be the expected share of students for the departments after two months have elapsed (i.e. in month 3)2What is the long-run pr

In analyzing switching between different engineering degree programs for freshman, survey data has been used to estimate the following transition matrix for the probability of moving between departments each month: To Department DI D2 D3 From D 0.8 The current (month share of students for the department are S0%, 309 and 209 for departments DI,D2_ and D3 respectively _ What will be the expected share of students for the departments after two months have elapsed (i.e. in month 3)2 What is the long-run prediction for the expected share for each of the three departments? Would you expect the actual share to approach the long run prediction Or not (and why)?



Answers

A local community college offers a three-semester athletics training (AT) program. Suppose
that at the end of each semester, 75$\%$ of students successfully move on to the next semester
(or to graduation from the third semester) and 25$\%$ are required to repeat the most recent
semester.
$$
\begin{array}{l}{\text { (a) Construct a transition matrix to represent this scenario. The four states are (1) first }} \\ {\text { semester, (2) second semester, (3) third semester, (4) graduate. }} \\ {\text { (b) What is the probability a student graduates the program within three semesters? Four }} \\ {\text { semesters? Five semesters? }}\end{array}
$$
$$
\begin{array}{l}{\text { (c) What is the average number of semesters required to graduate from this AT program? }} \\ {\text { (d) According to this model, what is the probability of eventual graduation? Does that seen }} \\ {\text { realistic? }}\end{array}
$$

Everyone. So in this question, we've been given a set off summary statistics relating to universities on the percentage off freshman who graduate within the expected four years. Is that a first about these questions asking whether we would describe this distribution as symmetric or skewed? And so what we're gonna use is the median on the first and third court tiles to have a look at that as well. Is that me? The first thing we notice is that the mean it's less than the median, so it's already indicating some kind of skew, even though this is looking pretty close. So then we're looking at the 25th percentile, the 75th percentile in the media, and the gap between the 25th percentile on the median here is 10.75 so it's quite a big gap. Where it's got between the median and the third percentile is only 4.85 So you've got a much wider gap between the 25th percentile and the median on the 75 percentile in the media. And so we can see from the combination of those two things that this is left skewed. It's not symmetrical The second part of this question is asking about whether there are any outliers on what we can do to you. What? This out is great. It's offenses. And so we're gonna use the formula that says that that well, in a very concerted school time, minus 1.5 times thank you. Uh, on the third quarter, I'll lost 1.5 times. Like you, uh, these are offenses. Well, that is Do is they tell us whether or not on We expect things to be allies, if they're within events, is then there within the acceptable range. If the outside events is that we would consider him to be unusual and therefore outlines. So for this sort of data, we have key one. All those for, let's say, calculate the school, tell right so 74.75 minus 59 that suggest using the 3rd 1st quarter oil is equal to at 15.6. Now, the ease of using this formula here, I'm just going to click what, 1.5 times like you are is so 1.5 kinds 15.6 is equal to 23.4. So now we've got all the tools to construct defences. If I scroll down a little bit, we have a key one, which is 59 late. Once I minus 23 week for is equal to 35 0.75 But it's a very terrible, uh, defense is gonna use this third call tile five plus 23.4, where this 23 point ball comes from about five times seems sold. Rage. That gives us 98 point. So now we look back, uh, summer statistics over here, and we say, Okay, have we got any violent? Usually within 35.75 When we look at our minimum, we've got 43.2, which is way above 35 on we look at maximum here, you say Okay, if you got anything above 98.15 on the maximum is 87.4, which again is lower than this fence. So we find that we don't have any outliers in this set of data. The third part, this question is asking us to construct a box plot. And this is really easy using this summary data. Another minute, there's no out wires. We can go straight ahead and use this to construct about. So if I just move this down a whistle, we can work from here. So that's draw little space restored. Now, Amax meant that we can see over here is 87. So I'm gonna put 90 at the top here and then down at the bottom because our minimum is only 43. Make this 40 just here so a maximum can go near the top, Appear on our minimum, going to the bottom because I've already got one box. What to build? We don't have Teoh. Be too worried about exact proportions, although it's much easier to see this on squared paper with Rueda, which I would absolutely recommend. So the school tile is at 59 on the third course was 75. That's 74. So it is gonna find were fully where we think 60 would be. So this is going up. 50 said that would be plus 20 by. There's gonna be a little bit under here. So says that that's me just working at my scale slightly and then the 75th quarter 74. So if we're saying that this is civil 65 74 is gonna be about here. There's our books, financial problems goes. And then the median that we found here 69 was much closer to the course. All level. That's good. What's gonna sit just here on this is the box part that we've constructed using this data now. Previously, I made a box plot in sum's stuff rippled You can see here, which just compares a little bit with the one that we've drawn. It's just so you can see a problem one without the sort of rough edges. Um on you can see this is drawn pretty well, and you can definitely see the difference in the height of the median being much closer to the top of this, integral to our range on. That's really indicating that left scheme so it wouldn't ask Teoh. Write a few sentences. And so what you want to talk about is that off the 48 universities that's account here that we were surveyed for this on average, about 68% off the freshmen graduate on time. We know that from this off mean median value here and with the range off the percentages of you of universities goes from about 43% 7% and that's a percentage off graduating freshman. But within those universities on the middle, 50% of universe to universities graduate 59 to 75% or freshman within the four years.

Working. Look at a survey results of a survey, Um, that was taken asking MBA students whether or not they apply to more than one school. They originally gave you a table, and they've asked you now to create a joint probability table out of the information they had. So this is question number 52. They gave you, um, a table and one of the columns are actually two of the columns said applied to more than one that was broken down into a yes and no column, and they separated it out. Based on age groups, they said 23 up under, and they did 24 to 26. 27 to 30 already won 2 35 and then h 36 older. What they had in the columns as they had zero point 1026 Free. Yes, 0.996 0.1482 0.1875 and then they had zero point is your own 917 0.13 to 8, 0.3 to 7, 0.956 and 0.253 and 0.837 These columns all totaled 20.4004 and 0.5996 So what we're gonna actually do know is we're going to create another column and this is gonna be a totals column. We're just gonna add across. So the total for the 23 under is gonna be a 0.20 to 2. 24 to 26. It's gonna be a 0.3360 when you summoned 2 30 is gonna be 0.2245 and then we're gonna have 0.1283 zero point 1090 We're gonna total that up and it's gonna be 1.0 100 And if you notice the total for the yes column when added to the total of the no column also totals up to 1.0 So heart be I asked you. But the probability of being, um under 23 Well, you look at that table and all we need to d'oh is take that total column and that one is gonna then be 0.20 to 2. See? Asked with the probability of being over 26 again look at the total column for the, um, you'll have to actually add up several of, um so you're gonna add a total column of 27 to 30 which is 0.2245 We're gonna add the 31 to 35 which is 0.1283 And we're gonna add, um 36 older, which is 0.1090 And that is going to told total up to zero point or 6 1/8 So that's the probability. Be up being over age 26 the next quip Part of this question, they asked what the probability ah, applying to more than one would be. And all we have to do is go down to the total of the yes column, and that number is gonna be zero point or 004 So that's the probability of applying to more than one school

Yeah. Hello. Hi hearing this question. We have been given a model which shows distribution of doctoral degrees. So in the first part of the question we have to verify the given data represent the probability model right for doing that. What we need to do is if it is a property model, All probabilities should be between zero and what you can see for engineering, physical science, lives has everything is Cuban here Can see all these values between zero and 1 admits that parties. Right. Second thing you have to verify is if you take some of all probabilities to take some of all probabilities or or we can say all the assembly points in that example space should be equal to one. So what are you going to do is I'm going to add all this When you add all these will be getting zero 00. What things were getting one, one is coming means cattle properties is 21. So what we can say both these conditions are satisfied. So we can say it is a property model and it is verified. The second part is asking us what is the probability a randomly selected doctoral candidate who have studied? What? Physical science or life science? It's a property of physical science or life size. When you find that probability you can see physical science, the cases point to 101 plus life science 0.206. This will be the answer. So we have to we don't have to consider the case of intersection here because both degrees cannot be taken at a time. Right? So when you add this week it .307. Now all the third part of the question we need to find the probability if that degree is taken. Mhm. Yeah. Yes I agree. It's physical science, life science mathematics or computer science. So we have to consider all this case. Physical science cambodia signs, life signs and finally mathematics. These four kids we had to add The answer to be getting is .101 plus 0.206 plus 0.24 plus zero point. You know what? So the submission of all these values will be the required answer. So when you add all this what answer you're beginning is 0.206 U. N. Plus 0 to form plus 0- one. Violence targeting is 0.352. That will be cancer for a second. But no the next question is asking what is the problem to that? That degree earned did not study mathematics. It is we have to find the complement of studying mathematics By a complimentary studied. It is equal to 1 -1 studied Madrid. It's It's 1- Mathematics case. You can see 0.024. That's a really big thing is 1 0 to form. That is around 0.976. This many cases that they're not studied mathematics? The last part of the question our doctor degrees in mathematics unusual. Does this result surprising? Okay, so you can see Doctoral degree only taken by very small quantity. That is 0.0. Mhm. 24. Only these many people are taken out of 100 people. That means it is less than 0.05. Eyeballs can see this very unusual. Right? As it is unusual. It is definitely surprises because the number of people taking mathematics mathematical doctorate is very let's compare two. Although sciences. Right. I hope the same studio question. Thank you.

In question 16. It says suppose there are 30 people at a party. Do you think any of them have the same birthday? So we're gonna use a random number table to simulate the birthdays of the 30 people at the party. We're gonna ignore leap year so that there's this Onley 365 possible days. We're gonna let one represent January 1 to represent January 2 and so on so that the last day of the year, December 31st, is 365. So these days represented birthdays that the people of the people at the party or any of the two birthdays the same. Compare your results with those obtained by other students in the class. Would you expect the results to be the same or different? So there's a few different ways. If you're doing the random number table, you can look across at, um, 33 digit values. So we have the values 001 through 3 65 representing all of the days of the year because 3 65 is a three digit value. We must have everything as a three digit value as we look from left to right across the random number table. We're gonna look at each three digit number and just determine if we can use that or not. We can use it if it's in the strange. If we get the values 000 or 3. 66 through 9 99 we can't use these values. We must skip them. So, um, as you look through and you pick out 30 different values that represent these birthdays, um, I did this in a few different trials. So trial one, I found zero matching birthdays. But in a second trial, uh, found zero matching birthdays in a third trial. I did found one matching birthday. So if you were looking at this or comparing this with your class, it's not unusual to find. Imagine birthday in a random sample of 30 people. Eso The question ultimately is, Would you expect the results to be the same or different as you compare them with anybody in your class? So you would expect that each student would get different and you would expect to have 30 different values for each of the students. But it wouldn't be uncommon to find that multiple students did find a match in terms of birthdays within the groups, so I'll say, if anything, other people to have results that have repeated birthdays.


Similar Solved Questions

5 answers
Q5.Solve any one of the following question a) Apply Lagrange' s linear equation method to solve the partial differen equation x(z2 yz)p + y(x2 22)q =Z(y2 x2) , where p and q have their usual meaning
Q5. Solve any one of the following question a) Apply Lagrange' s linear equation method to solve the partial differen equation x(z2 yz)p + y(x2 22)q =Z(y2 x2) , where p and q have their usual meaning...
3 answers
The elasticity values of two independent different lypes products Jie analyzed: Elasticily Droquci nas mu zb and Siguna_I= 15 whereas @lasticily product nasm 130 nd sigma Z= 35. Random samples of n_1-25 prcducts ard n2=49 products are selerted: Wnai the probabilily tHal mU_Z>inu_17Your answer:0,2460,75440.7880,909
The elasticity values of two independent different lypes products Jie analyzed: Elasticily Droquci nas mu zb and Siguna_I= 15 whereas @lasticily product nasm 130 nd sigma Z= 35. Random samples of n_1-25 prcducts ard n2=49 products are selerted: Wnai the probabilily tHal mU_Z>inu_17 Your answer: 0...
5 answers
Thc lifctimc of machine is continous On the interval (0, 40) with probability density function where f(t) is proportional to 10) and is the lifetime in Teears Calculate the prohability that the lifetime of the mac hine Dunt less than 10 FCArS- Hint: Shou that f() lcgitimate and find the popottionality constant.
Thc lifctimc of machine is continous On the interval (0, 40) with probability density function where f(t) is proportional to 10) and is the lifetime in Teears Calculate the prohability that the lifetime of the mac hine Dunt less than 10 FCArS- Hint: Shou that f() lcgitimate and find the popottional...
5 answers
Experilnent 4mullunno5a with (2) M hydrochlorie acid R & cakciun curbunatc amnt uuctly and (b1 calculatlons; Uncludding Klum nevnt curbonele? Shol balnced chemical cuuriotsnWNA the mass 0ftk ali-dricd prduct Durtou M Lk nucr wilh yolr uoricts Prelab Rcport Questlon 6? If noL how €47 YoU LCce ee r For Lic Int; loc Or (DICua5 UXlY JcaCHEM Z0S LAB 4 Synthesis 9
Experilnent 4 mullunno5a with (2) M hydrochlorie acid R & cakciun curbunatc amnt uuctly and (b1 calculatlons; Uncludding Klum nevnt curbonele? Shol balnced chemical cuuriots nWNA the mass 0ftk ali-dricd prduct Durtou M Lk nucr wilh yolr uoricts Prelab Rcport Questlon 6? If noL how €47 YoU...
5 answers
Youhale HOOK 0l Icad at a tempcrature 100"and add It to 1OOg 0/ waterat 20"C, The specific heat af lead 4aoin Sunits andtthe boiling temperatur 327"@What the final tempcrature assume no hejt loss - the outside erwvironment? Setdegreesthere Ms some heat loss the outside air;how would the Tutultt 0i Dart chanre? | Sclect /
Youhale HOOK 0l Icad at a tempcrature 100"and add It to 1OOg 0/ waterat 20"C, The specific heat af lead 4aoin Sunits andtthe boiling temperatur 327"@ What the final tempcrature assume no hejt loss - the outside erwvironment? Set degrees there Ms some heat loss the outside air;how woul...
5 answers
Commercial grade HCI is diluted with water to get a solution of HCl which is 0.387 M and has density of 1.23 g/ mL. Calculate the molality of the solution_ [Atomic masses (g mol-') H = 1.008, Cl = 35.45]
Commercial grade HCI is diluted with water to get a solution of HCl which is 0.387 M and has density of 1.23 g/ mL. Calculate the molality of the solution_ [Atomic masses (g mol-') H = 1.008, Cl = 35.45]...
5 answers
For the following cell using the Debye-Huckel equation to get the activity coefficients:Cuts) | Cu(NO3)z (aq, 0.038 M) Mn(NO3)2 (aq, 0.094 M), HCI (aq, 0.04 M) MnOz (s) | Pt Calculate: a. The reaction quotient; QThe Ecell: What would be the equilibrium constant?
For the following cell using the Debye-Huckel equation to get the activity coefficients: Cuts) | Cu(NO3)z (aq, 0.038 M) Mn(NO3)2 (aq, 0.094 M), HCI (aq, 0.04 M) MnOz (s) | Pt Calculate: a. The reaction quotient; Q The Ecell: What would be the equilibrium constant?...
5 answers
How many gears must be sampled to obtain a 98% confidence interval for the population mean impact strength of the gears provided by a supplier for the margin of error (half width) of 1.2 Nm? Assume that the population standard deviation is 15. Answer: n = [A].
How many gears must be sampled to obtain a 98% confidence interval for the population mean impact strength of the gears provided by a supplier for the margin of error (half width) of 1.2 Nm? Assume that the population standard deviation is 15. Answer: n = [A]....
5 answers
Two 2.9-pF capacitors_ 20 kIl resistors, and 20.0-V source connected series:Part AStarting from the uncharged state , how long does take for the current t0 drop from its initial value t0 1.90 IA Express your answer to two significant figures and include the appropriate unitsValueUnitsSubmitRequest Answer
Two 2.9-pF capacitors_ 20 kIl resistors, and 20.0-V source connected series: Part A Starting from the uncharged state , how long does take for the current t0 drop from its initial value t0 1.90 IA Express your answer to two significant figures and include the appropriate units Value Units Submit Req...
5 answers
Signibcnt enugh settion of interstate bighway that a5 (9 points} Tbe number of cacks in 4 meun of % cracks per mie; Poisrou distriburion with { mqure repair i5 ussumed tD fllow e significant enough @ requre X =the mmber of cacks per mile on the interstate highway thatcracks that require re (3 points) Wbat is the probability that there are seven pair in & mile of highway?in ? probability tbat at Leeetops crack requires repair points) Whbat % tbe miles o bigheay?
signibcnt enugh settion of interstate bighway that a5 (9 points} Tbe number of cacks in 4 meun of % cracks per mie; Poisrou distriburion with { mqure repair i5 ussumed tD fllow e significant enough @ requre X =the mmber of cacks per mile on the interstate highway that cracks that require re (3 point...
4 answers
Cos(x) Vyproblem initial value _ Solve the Problem=0Answer:
cos(x) Vy problem initial value _ Solve the Problem =0 Answer:...
5 answers
Chloroform, once used as an anesthetic agent;, has a density of 1.474 g/mL What volume would you use if you needed 0.0150 kg?O 1.02 x 10-5 mL0.0102 mL0.0221 mL22.1 mL10.2 mL
Chloroform, once used as an anesthetic agent;, has a density of 1.474 g/mL What volume would you use if you needed 0.0150 kg? O 1.02 x 10-5 mL 0.0102 mL 0.0221 mL 22.1 mL 10.2 mL...
5 answers
Are the following true or false? If true, give reason: If false; give cuunterexample:det( T + A) = 1+det A, for every 3 3 matrix A. det(4A) = 4det( A) for every 5 5 matrix A, For every 2 x2 matrices Aand C,if AC = Othen either A = Oor C = Owhere Ois the 2x2zero matrix_ For every 3 x 3 matrix A ifdet(4?) = 0 then det(A) = 0.
Are the following true or false? If true, give reason: If false; give cuunterexample: det( T + A) = 1+det A, for every 3 3 matrix A. det(4A) = 4det( A) for every 5 5 matrix A, For every 2 x2 matrices Aand C,if AC = Othen either A = Oor C = Owhere Ois the 2x2zero matrix_ For every 3 x 3 matrix A ifde...
5 answers
OX 44 4t 4a 0.50 _yllThe Range of the following data -7, 12,21, 11,1O, 13,-12 isJp#pAbill _Uisl A. 21B,10 0 C.33 0 D. 14 0
OX 44 4t 4a 0.50 _yll The Range of the following data -7, 12,21, 11,1O, 13,-12 is Jp#p Abill _Uisl A. 21 B,10 0 C.33 0 D. 14 0...

-- 0.019084--